It is known that a general solution for the position of aharmonic oscillator isx(t) = C cos (wt) + S sin (wt),where C, S, and ware constants. (Figure 2)Your task, therefore, is to determine the values of C, S,and w in terms of k, m,and init and then use theconnection between x (t) and a (t) to find theacceleration.FigureLminx=0Xinit1 of 2>Part ACombine Newton's 2nd law and Hooke's law for a spring to find the acceleration of the block a (t) as a function of time.Express your answer in terms of k, m, and the coordinate of the block x (t).► View Available Hint(s)a (t) =Submit17 ΑΣΦPart B Complete previous part(s)Review | Constants?

Answered: Image /qna-images/answer/058b36d7-07a0-46cc-bcf3-a068ffd0f009.jpg

It is known that a general solution for the position of a harmonic oscillator is x(t) = C cos (wt) + S sin (wt), where C, S, and w are constants. (Figure 2) Your task, therefore, is to determine the values of C, S, and win terms of k, m,and init and then use the connection between x (t) and a (t) to find the acceleration. Figure L win Xinit < 1 of 2 Part A Combine Newton's 2nd law and Hooke's law for a spring to find the acceleration of the block a (t) as a function of time. Express your answer in terms of k, m, and the coordinate of the block x (t). View Available Hint(s) a (t) = Submit [5] ΑΣΦ Part B Complete previous part(s) Review | Constants ?

It is known that a general solution for the position of a harmonic oscillator is x(t) = C cos (wt) + S sin (wt), where C, S, and w are constants. (Figure 2) Your task, therefore, is to determine the values of C, S, and win terms of k, m,and init and then use the connection between x (t) and a (t) to find the acceleration. Figure L win Xinit < 1 of 2 Part A Combine Newton's 2nd law and Hooke's law for a spring to find the acceleration of the block a (t) as a function of time. Express your answer in terms of k, m, and the coordinate of the block x (t). View Available Hint(s) a (t) = Submit [5] ΑΣΦ Part B Complete previous part(s) Review | Constants ?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Consider the solution tothe harmonic oscillator given above by x(t)=Ccos(wt−v) Prove tha tx(t0)=x(t0+2piw) In other words, the solution has the same value at time:t0 and at time:t0+2piw regardless of what value we have for ?0. The value 2piw is then the period T of the harmonic oscillator.
My system is a pendulum attached to moving horizontal mass m_1 and the pendulum m_2 that is shifted by X_o from origin. I have the lagrangian of my system what would be my equations of motions in terms of small angle approximation and what’s is their frequency?
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The quantities A and p (called the amplitude and the phase) are undetermined by the differential equation. They are determined by initial conditions -- specifically, the initial position and the initial velocity -- usually at t = 0, but sometimes at another time. In the oscillating part of the experiment, I measured only the time of 30 periods. I measured no position or velocity. Consequently, A and p (and also yo) are irrelevant in the problem. We only compare the period T or the frequency w with the theoretical prediction. You have (hopefully) derived (or maybe looked up) the relation between w and k and m. This final question relates w and T. If w = 5.8*10° rad/s, calculate T in seconds. (Remember, that a radian equals one.) T might be a fraction of a second.
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