Question

What is the average speed of a particle performing linear s.H.M of amplitude 'a' over one oscillation?

Answer 1

Answer:

The average speed of a particle performing linear S.H.M of amplitude 'a' over one oscillation is zero.

The relation of displacement of that particular particle is x(t) = a*sin wt

And the derivative of displacement with respect to time gives us the speed of the particle;

dx(t)/ dt = v(t)

v(t) =d[a*sin wt]/ dt = a*w*cos wt

v(t) = a*w*cos wt

So one oscillation the time period is one so the upper relation gives us the value zero.

Answer 2

The average velocity over one oscillation is zero not average speed.

Average speed = (total distance) /(total time)

v(av) = 4a/T

Where T=time period