A particle executes simple harmonic motion according to equation

Asked by admin @ 17/08/2021 in Physics viewed by 300 People

A particle executes shm according to equation x=10cos[2t+/2] , where t is in second. The magnitude of the velocity of the particle at t=1/6s will be:

Answered by admin @ 17/08/2021

Given equation,

x = 10cos(2t + π/2)

Differentiating both sides of the equation with respect to time.

We get,

v = 10 × 2 -Sin(2t + π/2)

∴ v = -20Sin(2t + π/2)

v = -20Sin(2 × 1/6 + π/2)

∴ v = -20Sin( π/2 + 1/3)

v = -20Cos(1/3)

v = -20 × 0.18

∴ v = -3.60 m/s.

Hence, the velocity of the particle at time 1/6 seconds is 3.6 m/s.

Hope it helps .

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