Question

A particle starts oscillating simple harmonically from its equilibrium position with time period T. At time t = T/12, the ratio of its kinetic energy to potential energy is ______.

`[sin  pi/3 = cos  pi/6 = sqrt3/2, sin  pi/6 = cos  pi/3 = 1/2]`

विकल्प

• 4 : 1

• 3 : 1

• 1 : 4

• 2 : 1

Answer 1

A particle starts oscillating simple harmonically from its equilibrium position with time period T. At time t = T/12, the ratio of its kinetic energy to potential energy is 3 : 1.

Explanation:

When t = `T/12`, then x = Asinωt = Asin`(2pi)/T.t`

`Asin  (2pi)/T xx T/12 = Asin  pi/6 = A/2`

KE = `1/2mv^2 = 1/2momega^2(A^2 - x^2)`

= `1/2momega^2(A^2 - A^2/4) = 3/4(1/2momega^2A^2)`

and PE = `1/2momegax^2 = 1/4(1/2momega^2A^2)`

∵ `(KE)/(PE) = 3/1`