Which of the following expressions corresponds to simple harmonic...

Which of the following expressions corresponds to simple harmonic motion along a straight line, where

x

is the displacement and

a, b, c

are positive constants?

Options

A $a+b x-c x^{2}$
B $b x^{2}$
C $a-b x+c x^{2}$
D $-b x$

Correct answer

D. $-b x$

Step-by-step solution

In linear S.H.M., the restoring force acting on particle should always be proportional to the displacement of the particle and directed towards the equilibrium position. i.e.,

\mathrm{F} \propto \mathrm{x}

\mathrm{F}=-\mathrm{bx}

where

\mathrm{b}

is a positive constant.

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