Investigate the Sly Pupil

A student says that he had applied a force F = - k x \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 has worked only with positive x and no other force acted on the particle.

Which of the following statement is correct?

As x increases k remains constant. The motion cannot be simple harmonic. As x increases k increases. As x increases k decreases.

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