Two children are playing on the swings in the friendly neighbourhood park. A claim is made by a student that the swingcan be modeled by forced harmonic motion (i.e. simple harmonic motion that is being pushed).Using this model, the horizontal position P of the swing relative to center of the swing structure is given by:P = A(w) · cos(wt)where t is time (in seconds), w is the frequency (in radians per second) at which the swing is pushed, and the directionthe children are facing is the positive direction. Also, A is the amplitude (in meters) of the swing, as a function of w:A(w) =3(2-w)In summary, at time t and with a pushing frequency of w, the horizontal distance of the swing from the centre line, isgiven by P A(w) cos(wt).1. FinddAAt pushing frequency w = 1 is this derivative positive, negative, or zero, and what does this indicateduphysically?2. Now suppose w is constant.dP(a) FindWhat do these derivatives represent?anddtd(b) EvaluatedPandfor t 4 and w 1. Use your answers to determine whether the swing is speedingdtdrup or slowing down, and in which direction.

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the swing relative to center P = A(w) - cos(wt) COS

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 1OQ: Which of the following statements is not true regarding a massspring system that moves with simple...

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