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?

a + b x - c x^{2}

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b x^{2}

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a - b x + c x^{2}

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- b x

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Solution

The correct option is A $- b x$
In case of a simple harmonic motion, the equation should be a linear polynomial in terms of the displacement. This can be understood using the Hooke's law F=-kx.
Hence, the expression that correctly explains SHM is $- b x$

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