If equation of displacement of aparticle is `y = A sinQt + B cosQt` then find the nature of the motion of particle.
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`y = AsinQt + BcosQt` Differentiate with respect to `t , (dy)/(dt) = AQ cos Qt - BQ sinQt` Again differentiating with respect to `t = (d^(2)y)/(dt^(2)) = Q^(2)A sinQt - Q^(2) B cos Qt` `(d^(2)y)/(dt^(2)) = - Q^(2) (AsinQt + BcosQt) rArr (d^(2)y)/(dt^(2)) = - Q^(2)y rArr (d^(2)y)/(dt^(2)) + Q^(2)y = 0` It is a differential equation of linear `S.H.M.` So motion of the particle is simple harmonic
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