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(C) motion represents simple harmonic motion $(SHM)$ if it is governed by the force law:$F = -kx \Rightarrow ma = -kx$$	herefore a = -\left(\frac{k}{

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$a=-10 x$

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(C) motion represents simple harmonic motion $(SHM)$ if it is governed by the force law:$F = -kx \Rightarrow ma = -kx$$	herefore a = -\left(\frac{k}{m}ight)x$Where:$F$ is the restoring force.$m$ is the mass of the body (a constant).$x$ is the displacement from the equilibrium position.$a$ is the acceleration.$k$ is the force constant.For $SHM$,the acceleration $a$ must be directly proportional to the negative of the displacement $x$ $(a \propto -x)$.Among the given equations,only $a = -10x$ follows the form $a = -\omega^2 x$,where $\omega^2 = 10$.Therefore,the correct relationship is $a = -10x$.

Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle involve simple harmonic motion?
$(a)\; a=0.7 x$
$(b)\; a=-200 x^{2}$
$(c)\; a=-10 x$
$(d)\; a=100 x^{3}$

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Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle involve simple harmonic motion?$(a)\; a=0.7 x$$(b)\; a=-200 x^{2}$$(c)\; a=-10 x$$(d)\; a=100 x^{3}$