A particle executes simple harmonic motion of amplitude A. (i) At what distance from the mean positio is its kinetic energy equal to its potential energy? (ii) At what points is its speed half the maximum speed?

Explanation

(i) `1/2momega^(2)(a^(2)-y^(2)) = 1/2momega^(2)y^(2) Rightarrowy=a/sqrt2 `
(ii) `v=omegasqrt(a^(2)-y^(2)) Rightarrow alphaomega = omegasqrt(a^(2)-y^(2)) Rightarrow y = + asqrt3/2`.