A student says that he had applied a force F = - k$\sqrt$(x) on a particle and the particle moved in simple harmonic motion. He refuses to tell whether k is a constant or not. Assume that he was worked only with positive x and no other force acted on the particle.

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KollegeApply · Accepted Answer

As x increases k increases. A body is said to be in simple harmonic motion only when, F = -kx ...(1) where F is force, k is force constant, and x is displacement of the body from the mean position. Given: F = -k$\sqrt$(x)...(2) On comparing the equations (1) and (2), it can be said that in order to execute simple harmonic motion, k should be proportional to $\sqrt$(x) . Thus, as x increases k increases.

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