Question

show that a linear shm is the projection of ucm on its diameter
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Answer 1

$\bold\orange{❥ᴀ᭄ɴsᴡᴇʀ:⤵}$

It shows that acceleration of particle M is directly proportional to its displacement and its direction is opposite to that of displament. Thus particle M performs simple harmonic motion but M is projection of particle performing U.C.M. hence S.H.M. is projection of U.C.M. along a diameter, of circle.

$\huge \colorbox{red}{❥ᴛʜᴀ᭄ɴᴋs}$