JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Elasticity & SHM

An object of mass 0.5 kg executing simple harmonic motion. Its amplitude is 5 cm and time period

(T)

is 0.2 s. What will be the potential energy of the object at an instant

t = \frac{T}{4}

s starting from mean position. Assume that the initial phase of the oscillation is zero.

Answer: (B)

Solution

With zero initial phase the displacement is

x = A sin ω t

. At

t = \frac{T}{4}

the phase is

\frac{π}{2}

, so

x = A

: the object is at the extreme position and its whole energy is potential.

U = \frac{1}{2} m ω^{2} A^{2}, ω = \frac{2 π}{T} = \frac{2 π}{0.2} = 10 π rad s^{- 1}

U = \frac{1}{2} \times 0.5 \times (10 π)^{2} \times (0.05)^{2} = 0.62 J

The potential energy of the object at that instant is

0.62

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Single correct option