question_answer 6)

Which of the following relationships between the acceleration, a and the displacement x of a particle involve simple harmonic motion. (a)\[\text{3cos}\left( \frac{\text{ }\!\!\pi\!\!\text{ }}{\text{4}}\text{-2 }\!\!\omega\!\!\text{ t} \right)\text{=3cos}\left( \text{2 }\!\!\omega\!\!\text{ t-}\frac{\text{ }\!\!\pi\!\!\text{ }}{\text{4}} \right)\] (b)\[\left[ \because \cos \left( -\theta \right)=\cos \theta \right]\] (c) \[a=-10x\] (d) \[\text{2 }\!\!\pi\!\!\text{ /2 }\!\!\omega\!\!\text{ }\text{.}\]

Answer:

In S.H.M., acceleration a is related to displacement by the relation of the form \[a=-kx\], which is for relation (c).