JEE Main · 2007 · 29 Apr 2007 · Offline · Elasticity & SHM

The displacement of an object attached to a spring and executing simple harmonic motion is given by

x = 2 \times 1 0^{- 2} cos π t

metres. The time at which the maximum speed first occurs is

Answer: (A)

Solution

The displacement is

x = 2 \times 1 0^{- 2} cos (π t)

, so the velocity is its time derivative,

v = - 2 \times 1 0^{- 2} π sin (π t)

. The speed is greatest when

∣ sin (π t) ∣ = 1

, which first occurs when

π t = \frac{π}{2}

. That gives

t = 0.5

s as the first instant at which the maximum speed is reached.

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option