Question

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

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

Answer 1

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
$F_{net}=-kx....\left(1\right)$
For a particle executing SHM, mean position is the point of equilibrium. Hence, the net force acting on it is equal to zero.
From $\left(1\right)$, we can say that
$a=-\frac{k}{m}x=-{\omega }^{2}x$
i.e $a\propto -x$
$\Rightarrow \frac{dv}{dt}=v\frac{dv}{dx}=-{\omega }^{2}x$
Doing integration on both sides, we get
$v=\pm \omega \sqrt{A^2-x^2}$
$\therefore$ 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.