The amplitude of a particle executing SHM about O is 10 cm. Then: This question has multiple correct options

When the K.E. is 0.64 of its max. K.E. its displacement is \( 6 \mathrm{cm} \) from 0 .
When the displacement is 5 cm from 0 its K.E. is 0.75 of its max.P.E.
Its total energy at any point is equal to its maximum K.E.
Its velocity is half the maximum velocity when its displacement is half the maximum displacement.

Correct answer: When the K.E. is 0.64 of its max. K.E. its displacement is \( 6 \mathrm{cm} \) from 0 .

Solution

In SHM, \(K = K_{\max}(1 - x^2/A^2)\). Setting \(K = 0.64K_{\max}\) gives \(x^2/A^2 = 0.36\), so \(|x| = 0.6A = 6\) cm. This matches the given correct option.

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