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

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

\mathrm{x}

is the displacement and

\mathrm{a}, \mathrm{b}, \mathrm{c}

are positive constants?

Options

A $a+b x-c x^2$
B $\mathrm{bx}^2$
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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