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Question

Which of the following statement is incorrect for a particle performing linear SHM?

A
Acceleration is always directed opposite to the direction of displacement.
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B
Velocity of the particle is constant.
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C
The net force on the particle is zero at mean position.
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D
Acceleration is proportional to the displacement from mean position.
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Solution

The correct option is B Velocity of the particle is constant.
If a particle executes SHM about mean position x=0, we can say that
Fnet=kx ....(1)
For a particle executing SHM, mean position is the point of equilibrium. Hence, the net force acting on it is equal to zero.
From (1), we can say that
a=kmx=ω2x
i.e ax
dvdt=vdvdx=ω2x
Doing integration on both sides, we get
v=±ωA2x2
we can say that, the velocity of particle executing SHM is not constant and is a function of the position of the particle.
Thus, option (b) is incorrect.

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