Question

Average velocity of a particle performing shm in one time period is?

Answer 1

Simple harmonic motion can be expressed as follow:

y=a*cos(w*t) where w is angular acceleration and

w=2*pi/T

So, when we differentiate the above equation we get expression of velocity given by:

v=-a*w*sin(w*t)

For a complete time period,

t=T

So,

The average velocity= -a*w*(average of sin(w*t) over time period T)

Average of Sin function over a complete cycle=0

Therefore,

The average velocity of a particle performing S.H.M. in one time period is 0.

Answer 2

In one time period

the particle returns back to its mean position
so, X=0

as, avg.V= total X/total time

avg.V=0

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