If the displacement ( x ) and velocity ( v ) of a particle executing SHM are related through the expression 3 v 2 = 30 - x 2 . If the time period of the particle is T = π n , then what is the value of

Question

If the displacement ( x ) and velocity ( v ) of a particle executing SHM are related through the expression 3 v 2 = 30 - x 2 . If the time period of the particle is T = π n , then what is the value of n ?

TestHub · Accepted Answer

Given equation, 3 v 2 = 30 - x 2 Differentiating both sides, we get 6 v d v d x = - 2 x ⇒ v d v d x = - 1 3 x ⇒ a x = - 1 3 … ∵ a = d v d t = d v d x d x d t = v d v d x T = 2 π acceleration displacement = 2 π - 1 3 = 2 π 3 = π 12 n = 12

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