Two children are playing on the swings in the friendly neighbourhood park. A claim is made by a student that the swing can 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 direction the 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 -) In summary, at time t and with a pushing frequency of w, the horizontal distance of the swing from the centre line, is given by P= A(w) cos(wt). 1. Find dA At pushing frequency w = 1 is this derivative positive, negative, or zero, and what does this indicate dw physically? 2. Now suppose w is constant. dP (a) Find dP and dt What do these derivatives represent? dP and dt (b) Evaluate for t= 4 and w= 1. Use your answers to determine whether the swing is speeding dt up or slowing down, and in which direction.

Two children are playing on the swings in the friendly neighbourhood park. A claim is made by a student that the swing can 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 direction the 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 -) In summary, at time t and with a pushing frequency of w, the horizontal distance of the swing from the centre line, is given by P= A(w) cos(wt). 1. Find dA At pushing frequency w = 1 is this derivative positive, negative, or zero, and what does this indicate dw physically? 2. Now suppose w is constant. dP (a) Find dP and dt What do these derivatives represent? dP and dt (b) Evaluate for t= 4 and w= 1. Use your answers to determine whether the swing is speeding dt up or slowing down, and in which direction.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.7: Applied Problems

Problem 68E

See similar textbooks