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 a∝−x ⇒dvdt=vdvdx=−ω2x Doing integration on both sides, we get v=±ω√A2−x2 ∴ 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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