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Q. 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 ?

JEE MainJEE Main 2014Oscillations

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., $F\,\propto\,x$
or $F=-bx$ where $b$ is a positive constant.