Please show me all the steps The shadow of a particle undergoing uniform circula

Question

Please show me all the steps

The shadow of a particle undergoing uniform circular motion executes SHM as discussed in class. The radius of a reference circle is 5.0 m. The frequency of the SHM of the shadow is 4.5 Hz. Calculate (a) angular frequency in radians/sec, (b) period in sec, (c) the position at t = 4/9 sec, (d) the magnitude of velocity at t = 6/9 sec, (e) the magnitude of the acceleration of the shadow at t = 8/9 sec. (Use f = 9/2 Hz in the intermediate calculations for exact answers.) Write expressions for x = f(t), v = f(t), and a = f(t) and plot two cycles for each.

Explanation / Answer

For the SHM:

amplitude = radius = 5m

frequency = 4.5 Hz

a) angular frequency, w = 2*pi*f = 2*3.14*4.5 = 28.26 rad/s

b) period = 1/f = 1/4.5 = 0.22 s

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