A particle is executing simple harmonic motion. What is phase relationship between velocity and acceleration?

Solution

Let the position of particle be given by,

space space space space space space space space space space space space space space space space space space straight y equals straight r space sin space ωt space therefore space straight v equals straight r space straight omega squared space sin space ωt space space space space straight a space equals space minus straight r space straight omega squared space sin space ωt space space space space space space equals space straight r space straight omega squared space cos space left parenthesis ωt space plus space straight pi divided by 2 right parenthesis

Therefore, velocity lags behind the acceleration by phase ϕ/2.

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