determine the vector representation of the couple shown

that a moment that causes the object to rotate counterclockwise is positive whereas a moment that causes the object to rotate clockwise is. /Type /FontDescriptor One force that acts horizontally /ItalicAngle 0 The Euler-Cauchy stress principle states that upon any surface (real or imaginary) that divides the body, the action of one part of the body on the other is equivalent (equipollent) to the system of distributed forces and couples on the surface dividing the body, and it is represented by a field (), called the traction vector, defined on the surface and assumed to depend continuously on the . 1.The tension in cableDA has a magnitude of TDA lb. c. 180, the horizontal and vertical components of several forces are: B) Generally coincides with the center of gravity for objects considered in engineering analysis if the gravitational field for all parts of the object is uniform and parallel. 0000003444 00000 n D) single force and a single moment. D) The value of the force cannot be determined by the Method of Joints. 60 3 m 2.72 Determine the magnitude of the single couple that is equivalent to the two couples shown 1.8 m B 60 2.73 Calculate the combined moment of the couple C and the force P about the axis AB. It may be helpful to rotate the triangle into this orientation: Now use trigonometry to express the side lengths and in terms of. /CapHeight 693 Three coplanar forces act on an object P, as illustrated in the Figure, F1=57 with an angle of 1, F2=2, F3=76. /Length 1442 Find the force due to the spring But if a second waveform starts to the left or to the right of this zero point or we want to represent in phasor notation the relationship between the two waveforms then we will need to take into account this phase difference, of the waveform. Forces acting on beam are 3KN, 2KN, 7 KN known and unknown external forces and couple moments that act on the body. If the red phase voltage, VRN is taken as the reference voltage as stated earlier then the phase sequence will be RYB so the voltage in the yellow phase lags VRN by 120o, and the voltage in the blue phase lags VYN also by 120o. Can you use phasors to analyze circuits with sinusoidal waveforms of negative frequency? /Parent 86 0 R negative. Explanation: The forces at B and C used to form a couple M is given by. These cookies track visitors across websites and collect information to provide customized ads. Hint 2. Express the individual components to three significant figures, if necessary, separated by commas. Express the individual components to three significant figures, if necessary, separated by commas. Identify the reaction forces at point A 4. Find the Cartesian components of tension TDA , which is directed from DtoA. The lengths of the phasors are proportional to the values of the voltage, (V) and the current, (I) at the instant in time that the phasor diagram is drawn. 0000000017 00000 n When we have a force shown with coordinate direction angles, all we need to do is multiply the force by the cosine of each angle to get the component. (b) Fh = 300lb and Fv = -200lb . Posted 6 months ago Q: Either way, one phasor is designated as the reference phasor and all the other phasors will be either leading or lagging with respect to this reference. reaction forces for each support type. /FontBBox [ -568 -216 2000 693 ] hb```f`` 0000002638 00000 n where is the spring constant and is the displacement or change in length of the spring. endobj Determine the moment of force F about point O. Grading Policy. Here r is any position vector from the line of action of the line of action ofF. /T 465858 Hint 1. Definition 2.1.5. triangle is a right triangle, we can use trigonometry and/or the Pythagorean theorem to express the unknown sides in terms of. supported at point A by a cable. A beam is a structural member that can: ANSWER: Hint 3. one couple applied. Redrawing the triangle Check all that apply. /Linearized 1 They can be converted from one to another as sine and cosine waves. Because there is only one couple, the moment can be calculated using the scalar method: where is the magnitude of the Given vector $v_1 = (8, -4)$, calculate the the magnitude. The length of The line of action of the 5- and the 4- forces goes through point B, so the calculation is simplified by taking the moment about So the difference between the two phasors representing the two sinusoidal quantities is angle and the resulting phasor diagram will be. %%EOF Figure 4.19b shows a closed-loop vector representation that can be formally used to obtain Eqs.(4.21). Find the moment of the couple acting on the rod FinalAnswer 57.2K subscribers Share 18K views 4 years ago Get the book here: https://amzn.to/2py6FIn Express the moment of the couple acting on. endstream endobj 168 0 obj <> endobj 169 0 obj <> endobj 170 0 obj <>stream . 2. Thus, phasor notation defines the effective (rms) magnitude of voltages and currents. Finding 3D forces/moments. endstream endobj 171 0 obj <>stream In principle of Moments experiment, test 1(equal distanced forces) is applicable to ____ /Length 154 << C) The direction that was chosen for the force was incorrect, and the correct direction of the force is opposite to the direction that was chosen in the analysis. Hint 1. For r as a position vector which runs from the moment reference point to any point on the line of action of a force F the moment M of the force about the point may be calculated as: From the free-body diagram, /StemV 42 We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. Note that the vector for a resultant force has a double arrowhead to distinguish it from the other forces acting in the system. Show your answers in graphucal and analytical method. /Filter /FlateDecode 19 - Foner, Eric. A direction cosine is: Shown. 333 389 278 500 500 722 500 500 444 0 200 ] the line segment. Fx =-200 i` N . 0000001802 00000 n Definition Force Couple: a pair of forces which are (i) equal in magnitude, (ii) parallel and (iii) opposite in direction. 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Wqn4@}C5/zU'" q B+WF%8lsn}uWi/qJ} Xf(A|M>K:J4>/$[Pi ++ (m-bR8r'A$GON=4MUg/ &QB(#> 8Nz7w{. Welcome to MathPortal. The proof of this will be learned Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. Find the angle between the vectors $v_1 = (3, 5, 7)$ and $v_2 = (-3, 4, -2)$. >> Moment = 600 N-m, A: Given data As one single rotation of the generator is 360o, each phase is therefore electrically seperated from each other by 120o. units. ANSWER: Indicate the force on the free-body diagram as a vector with the arrowheads at the point of contact of the resultant force. The force in a linear elastic spring is given by /CapHeight 677 >> B) Are always supported at their ends. Using similar triangles to find Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. Hint 1. Because the The arrowed end represents the quantity which freely rotates in an anti-clockwise direction at an angular velocity, (). Differentiating with respect to time gives: In . Frames and machines are always larger than trusses. A) Is always at the same point as the center of gravity. /AvgWidth 402 . Vectors Algebra Index. Comments 1). The forces at B and C used to form a couple M is given by. A: Let's consider the force 260 lb is making an angle ? Draw a Hint 1. (Jb!x: Spring equation << or X and Y. d. Cross), Give Me Liberty! D) Must be located on the object. Express your answer to three significant figures and include the appropriate units. Q) can be calculated using the scalar triple product. A balanced three-phase voltage supply consists of three individual sinusoidal voltages that are all equal in magnitude and frequency but are out-of-phase with each other by exactly 120o electrical degrees. 2. Xh1MI?{cZ)b{6&6O|2IxdvZbB[^SA|_aeR~q48q8B &[Q4 Y.^0-] 8v)88+7@.# If you want to contact me, probably have some questions, write me using the contact form or email me on endobj 3. >> Step-by-Step Verified Answer This Problem has been solved. A) M = r F . A: The problem will be solved in two parts and has been mentioned below. /Encoding /WinAnsiEncoding Psychology (David G. Myers; C. Nathan DeWall), Forecasting, Time Series, and Regression (Richard T. O'Connell; Anne B. Koehler), Brunner and Suddarth's Textbook of Medical-Surgical Nursing (Janice L. Hinkle; Kerry H. Cheever), The Methodology of the Social Sciences (Max Weber), Biological Science (Freeman Scott; Quillin Kim; Allison Lizabeth), Chemistry: The Central Science (Theodore E. Brown; H. Eugene H LeMay; Bruce E. Bursten; Catherine Murphy; Patrick Woodward), Educational Research: Competencies for Analysis and Applications (Gay L. R.; Mills Geoffrey E.; Airasian Peter W.), Business Law: Text and Cases (Kenneth W. Clarkson; Roger LeRoy Miller; Frank B. The center of mass and the center of gravity: /Contents 100 0 R I used a lot of vectors to make this game. 2. A beam is subjected to a triangular load distribution with a maximum pressure of. The horizontal side of a vector is equal to the real or x vector. Complete the free-body diagram of the beam by adding the missing forces acting on it. The two couples shown are to be replaced with a single equivalent couple. 3. Drawn to a scale of 1 cm =5 N, the vector representing F 1 will be 4 cm long and the vector representing F 2 will be 5 cm long. Force acting at point C =54 KN %PDF-1.5 % /Filter /FlateDecode In a simple truss for equilibrium the forces are assumed to be: /FontWeight 400 document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); I understand the fact that in 3 phase systems, the phase angle between each phase is 120 degrees, but why is that the voltage across 2 phase is 415volts??? In math, a vector is an object that has both a magnitude and a direction. To gain insight into the independence of the scalar triple product from the point on the line chosen as the reference point of the calculation. Can I get some revision questions on phasors and sinusoids. Recall that the tension in a cable (a) Ph= -200lb and Pv = 100lb : Thus, phasor notation defines the RMS magnitude of voltages and currents as they deal with reactance. Now that both the real and imaginary values have been found the magnitude of voltage, VT is determined by simply using Pythagorass Theorem for a 90o triangle as follows. Example: the sum of (1,3) and (2,4) is (1+2,3+4), which is (3,7), \begin{pmatrix}1&0&3\end{pmatrix}+\begin{pmatrix}-1&4&2\end{pmatrix}, (-3)\cdot \begin{pmatrix}1&5&0\end{pmatrix}, \begin{pmatrix}1&2&3\end{pmatrix}\times\begin{pmatrix}1&5&7\end{pmatrix}, angle\:\begin{pmatrix}2&-4&-1\end{pmatrix},\:\begin{pmatrix}0&5&2\end{pmatrix}, projection\:\begin{pmatrix}1&2\end{pmatrix},\:\begin{pmatrix}3&-8\end{pmatrix}, scalar\:projection\:\begin{pmatrix}1&2\end{pmatrix},\:\begin{pmatrix}3&-8\end{pmatrix}. Find the weight of the hanging mass when the spring, with spring constant , has been stretched. Remember, in a vector, there is a specific beginning and ending point, and the ending point is marked as an arrow. D) It is possible to solve for a maximum of four unknowns from a single free body diagram. ), Worksheet Problem 03.078 - /BaseFont /Times#20New#20Roman,Bold The formula for the dot product of vectors $ \vec{v} = (v_1, v_2) $ and $ \vec{w} = (w_1, w_2) $ is. that the moment of a couple is independent of reference points allows us to choose any reference point for our calculations. /Widths 96 0 R Calculate the magnitude of the resultant force and resultant moment for Case 1 Calculate the force, F4=?. Hint 2. By drawing out the two phasors to scale onto graph paper, their phasor sum V1+V2 can be easily found by measuring the length of the diagonal line, known as the resultant r-vector, from the zero point to the intersection of the construction lines 0-A. /Descent -216 The length of the line segment represents the magnitude of the vector, and the arrowhead pointing in a specific direction represents the direction of the vector. B) The moment produced by two forces which are perpendicular to each other. Frames and machines differ from simple trusses in that: You could say, "Look, we finished . 98 0 obj Let's start with force F_1 F 1. The dimensions are = 1 , = 1 , and = 1. D) The velocity of a particle is proportional to the vector sum of forces acting on it, and is in the direction of this vector sum. 3. Find instantaneous current and voltage in polar coordinates at indicated points. It does not store any personal data. couple is defined as two parallel forces with the same magnitude but opposite in direction separated by a perpendicular distance "d." The moment of a couple is defined as = F d (using a scalar analysis) or as O M = r (using a vector analysis). When writing the equations of equilibrium, recall that the weight acts only in the negative y direction: Hint 2. Force = 300N This cookie is set by GDPR Cookie Consent plugin. << Thus the line voltage, (VL) is measured as: (3) x 240V = 415V, or (3) x 120V = 208V. 333 500 556 278 333 556 278 833 556 500 556 556 444 389 333 556 500 722 0 Hint 1. It can be represented in the mathematical: Rectangular, Polar or Exponential form. or more multiforce member. How to calculate the moment The tension in rod BD is Thus phasor diagrams can be thought of as representing functions of time. 60 3 ft >> 2. magnitude of the moment. The x component of the 20- force has the magnitude and acts in the 8KN, 5KN, 3KN You can add, subtract, find length, find vector projections, find dot and cross product of two vectors. Using a ruler and protractor, draw an arrow to represent the first vector . ANSWER: Hint 3. seven operations on two dimensional vectors + steps. necessary to prevent P from moving. The hanging mass causes a tension of in For the 3, A: Given data as per the question Determine the vector representation of the couple /StructParents 47 A) Only three mutually perpendicular forces. Express the load /Type /Font Consider the phasor diagram below. Notify me of follow-up comments by email. Assume 60 But opting out of some of these cookies may affect your browsing experience. Express the individual components to three significant figures, if necessary, separated by commas. You can determine the couple moment as M = r x F C) rCB A general system of forces and couple moments acting on a rigid body can be reduced to a ___ . Two 80-N forces are applied as shown the comers ard D of a rectangular Plata (a) Determine the moment of the coupe formed bythe fomes by resolving each fcnce into hmimnta_ and vertical com}nnents adding the moments of the two lesulting coupley (b) Use the lesult obtained to determine the erFendicuIar distance be tween lines BE and DF As shown, a 2.7-lblbball is suspended at pointD inside a box with dimensions w=8.90 ft, ft, d=6.50ft . Find the cross product of $v_1 = \left(-2, \dfrac{2}{3}, 3 \right)$ and $v_2 = \left(4, 0, -\dfrac{1}{2} \right)$. Hint 1. 45 lb 99 0 obj To determine: Magnitude and direction of a single, A: Write the unit vector of the axis of moment M1. (a) Let R,Mo be the equivalent resultant, A: **As multiple questions are posted at a time, according to the guide-lines we can answer only one, A: Fx=0Rx=0Fy=0Ry=5-3-8=-6KNR=Rx2+Ry2=02+(-6)2=6KN, A: Given: /Resources << /Font << /F1 91 0 R /F2 94 0 R /F3 97 0 R >> /XObject << /X0 with the horizontal. Using the geometry shown in the figure below, determine the perpendicular distance between the forces,. A multiforce member must have: B) At least three applied forces and a couple acting on it. B) Are never the same on a given object. /Type /Page How to approach this problem 0000002965 00000 n The general process (not referenced to Figure 1) to calculate the moment of a force about a specified axis is as follows: The magnitude of a moment about a line segment connecting points, As shown in the figure, the member is anchored at, Which of the following equations correctly evaluates the scalar triple product of three Cartesian vectors, The dot product takes two vectors and returns a scalar given by, The cross product takes two vectors and returns a vector given by. C) The cosine of the angle used to calculate the scalar product of a vector. the spring constant and is the displacement of the spring from its original length. negative, negative, positive, Hint 1. B) Using the sum of the moments of the components of the force about the same point. 88 14 , The cross product of vectors $ \vec{v} = (v_1,v_2,v_3) $ and $ \vec{w} = (w_1,w_2,w_3) $ is given by the formula: Note that the cross product requires both of the vectors to be in three dimensions. D) Can be analyzed by the same techniques used to analyze trusses. ANSWER: The image below shows a beam subject to two couples, and. Each position along the horizontal axis indicates the time that has elapsed since zero time, t=0. iT5_~9dP5Y>g.AmXt,WM-n6-l]GSGaCU << Identify the applied loads Determine if the following set of vectors is linearly independent: $v_1 = (3, -2, 4)$ , $v_2 = (1, -2, 3)$ and $v_3 = (3, 2, -1)$. /FontDescriptor 95 0 R << )M88fY|Kzi0B&2in kg2h}tOtT}YKc-X 54 In a three-phase balanced system each individual phasor is displaced by 120. For each operation, calculator writes a step-by-step, easy to understand explanation on how the work has been done. axes given in the figure. negative, positive, positive Couple = 60 N-m, A: Appl the equilibrium of forces in the vertical direction. 4. Fy = 0 j`, A: Given data Linear combinations, which we encountered in the preview activity, provide the link between vectors and linear systems. The general process (not referenced to Figure 1) to calculate the moment of a force about a specified axis is as follows: The magnitude of a moment about a line segment connecting points P and Q due to a force applied at point R (with R not on the line through P and /FontBBox [ -558 -216 2000 677 ] pointDis the origin of the Cartesian coordinate system, pointA is located at (4.60,3.60,2.80)ft, point B is located at (1.90,3.60,1.90) ft, and point C is located at (1.90,5.30,1.70) ft. couple M are applied to corner A of the block shown. Standard practice is to colour code the three phases as Red, Yellow and Blue to identify each individual phase with the red phase as the reference phase. And net force would be, A: Data given - hbbd```b``"CA$~,~D2`/uE2"S&$H49S H2[j@_O pN Previously we have only looked at single-phase AC waveforms where a single multi-turn coil rotates within a magnetic field. This arises in induction generators and requires caution in circuit analysis for negative frequencies. Learn about Vectors and Dot Products. Please how is it calculated?? Necessary cookies are absolutely essential for the website to function properly. In math, a vector is an object that has both a magnitude and a direction. moving to the next part. By clicking Accept All, you consent to the use of ALL the cookies. Hint 3. The force at C to form a couple M is ( N) ( ). Two forces: one that acts perpendicular to the cable's direction and one that acts parallel to the cable Transcribed Image Text: Determine the vector representation of the couple shown 45 lb 60 3 ft A 1.8 ft B 60 45 lb Moment: Rotation (clockwise or counter clockwise): Expert Solution Want to see the full answer? Hint 1. Example 03: Calculate the dot product of $ \vec{v} = \left(4, 1 \right) $ and $ \vec{w} = \left(-1, 5 \right) $. The positions of the centroid and the center of mass: . These cookies will be stored in your browser only with your consent. Ma = ____ Lbft. Hint 1. What is the radius vector from A to B? If , , and Using phasor method of the moments about point B. Mathematically we can add the two voltages together by firstly finding their vertical and horizontal directions, and from this we can then calculate both the vertical and horizontal components for the resultant r vector, VT. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". Forces in Cartesian Vector Form Watch on Let's start with the first example: In this example, the force is shown with coordinate direction angles. Is the moment positive or negative? For this reason . Force-couples acting Vector Calculator. 1. endstream endobj 172 0 obj <>stream B) Support tension or compression and resist only bending. You can add, subtract, find length, find vector projections, find dot and cross product of two vectors. value of the sinusoidal quantity rather than its maximum value. B) Fx = 0, Fy = 0, Fz = 0, and the sum of moments about an axis normal to the plane is zero. D) A force in tension along the cable, belt, chain, or rope and a moment about the point at which the cable, belt, chain, or rope is connected to the object. Sum the forces in the x direction and the forces in the y direction. Equilibrium of the pulley Generally, when constructing a phasor diagram, angular velocity of a sine wave is always assumed to be: in rad/sec. C) Are the same for objects of non-uniform density. Express your answer to three significant figures and include the appropriate units. /XHeight 250 ANSWER: Learning Goal: determine each force and its angle with respect to the hozirontal (x-axis). Calculate the length of the unknown sides. Determine the equation of equilibrium (b) Use the result obtained to determine the perpendicular distance between lines BE and DF. B)Is the simplest force combination which can replace the original forces without altering the internal effect on the rigid body to which the original forces are applied. For example, if two voltages of say 50 volts and 25 volts respectively are together in-phase, they will add or sum together to form one voltage of 75 volts (50 + 25). opposite direction of the two 3- forces. /FirstChar 32 Two or more vectors can be added or subtracted together and become a single vector, called a. Get the book: http://amzn.to/2h3hcFq Show more Shop the FinalAnswer store Determine the moment of. %%EOF Solution : (A) Determine the Magnitude of the equivalent couple and the direction of its axes Step 1: Determine Equivalent Couple & Couple Vector (Beer et al.,2009) The magnitude of couple along X axis - Mx = 3 lb ft The magnitude of couple along Y axis - My = 0 The magnitude of couple along Z axis. They can be either voltage, current or some other alternating quantity but the frequency of all of them. Due: 8:20am on Thursday, November 7, 2019 The dimensions are , , , , and Generally the reference phasor is drawn along the horizontal axis and at that instant in time the other phasors are drawn. These cookies ensure basic functionalities and security features of the website, anonymously. > of 3 How to approach this problem Distance, d = 6 m Happiness - Copy - this is 302 psychology paper notes, research n, 8. ,CPr)AIiLrjtYPi{FU7r%!b_Em*w-37W#TCEOo? Tension in cable BC /E 4519 a. where is the magnitude of the force and is the perpendicular distance between the lines of force comprising the couple. shown; xc```b``Vg`a`` @1V %(!8Q# -``;+pY? must equal the force in the spring,. 2. A Cartesian vector representation of the equivalent couple is ( kNm) i + ( What can be said about the order of operations when evaluating the scalar triple product? portion of cable from point B to point C, , and the weight. << [ 250 333 408 0 0 0 0 0 333 333 0 564 250 333 250 278 500 500 500 500 500 /BaseFont /Times#20New#20Roman,Italic Hint 2. such an opportunity to learn this from you. units. << The magnitude of a vector 1 2. the 4- force. But we can also say the blue phase voltage, VBN leads the red phase voltage, VRN by 120o. . 4. B) Distributed uniformly along the length of the member. Hint 1. B) The forces must be collinear. Determine the vector representation of the couple shown. All contents are Copyright 2023 by AspenCore, Inc. All rights reserved. In both cases the phase angle, direction and angular velocity remains the same. A: The x component of the force can be determined as. >> 3. 45 1b This doesnt add up. A multiforce member must have: Draw the missing forces ending at the appropriate black dots. For a Delta connected generator (or transformer) the phase voltage equals the line voltage. 0 /Widths 93 0 R Vectors obey the parallelogram law of addition and subtraction so can be added together to produce a vector sum which rotates anticlockwise at an angular speed. Drag the appropriate items to their respective bins. /Widths 99 0 R /Subtype /TrueType 3. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. C) The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear. This website uses cookies to improve your experience while you navigate through the website. 4. + = 3. B) The acceleration of a particle is proportional to the vector sum of forces acting on it, and is in the direction of this vector sum. Hint 2. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. 45 lb The scalar triple product of the unit direction vector of the line segment, direction vector to the force, and the force vector gives the Forces applied at three or more points, or forces applied at two or more points and at least What are the x and y components of the resultant force, and and the magnitude of the resulting moment for Case 1? Calculate the magnitude of the resultant force and resultant moment for Case 3 /Leading 42 given force-couple system with an equivalent force-couple system at corner H. A Cartesian vector representation of the equivalent force at H is ( lb) i + ( For a three-phase supply, the magnetic field on the rotor of the generator links in sequence with three equally spaced windings, or phases, on its stator producing an equally spaced three-phase supply. Hint 3. How to approach the problem Seagull Edition, ISBN 9780393614176, Conversation Concept Lab Transcript Shadow Health, QSO 321 1-3: Triple Bottom Line Industry Comparison, Lab 1-Chemistry and Measurement-Lab Report, 446939196 396035520 Density Lab SE Key pdf, Test Bank Chapter 01 An Overview of Marketing, Sawyer Delong - Sawyer Delong - Copy of Triple Beam SE, Tina Jones Heent Interview Completed Shadow Health 1, EDUC 327 The Teacher and The School Curriculum, BI THO LUN LUT LAO NG LN TH NHT 1, cash and casssssssssssssshhhhhhhhhhhhhhhhh, Leadership class , week 3 executive summary, I am doing my essay on the Ted Talk titaled How One Photo Captured a Humanitie Crisis https, School-Plan - School Plan of San Juan Integrated School, SEC-502-RS-Dispositions Self-Assessment Survey T3 (1), Techniques DE Separation ET Analyse EN Biochimi 1. A complete sine wave can be constructed by a single vector rotating anti-clockwise at an angular velocity of =2, where denotes the frequency of the waveform. Activity #3: Moment of Force Are never located at the same point on an object. It will do conversions and sum up the vectors. O@)BJD @>ms.N-jH_=7v/A We can find the magnitude of a vector (when we know its components) by taking the square root of the sum of the squares of the components. This answer is expected from your /AvgWidth 401 where is a position vector from any point on the line through P and Q to R and is the unit vector in the direction of line segment PQ. Cartesian vector. /O 90 Example 3 (LiveMath) Sinusoidal waveforms of the same frequency can have a Phase Difference between themselves which represents the angular difference of the two sinusoidal waveforms. stellaris composer of strands,

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