The time period of a particle undergoing SHM is 16 s. It starts motion from the mean position. After 2 s, its velocity is 0.4 m s -1. The amplitude is

Question

The time period of a particle undergoing SHM is 16 s. It starts motion from the mean position. After 2 s, its velocity is 0.4 m s -1. The amplitude is (A) 1.44 m (B) 0.72 m (C) 2.88 m (D) 0.36 m

Tardigrade Admin · Accepted Answer

Velocity, v = r ω cos ω t 04=r × (2 π/16) cos (2 π/16) × 2=r × (2 π/16) × (1/16) × (1/√2) or r=(0.4 × 16 × √2/2 π)=(3.2 √2/π)=1.44 m

Q. The time period of a particle undergoing SHM is $16 s$ . It starts motion from the mean position. After $2 s$ , its velocity is $0.4 m s^{- 1}$ . The amplitude is

1.44 m

0.72 m

2.88 m

0.36 m

Velocity, $v = r ω cos ω t$
$04 = r \times \frac{2 π}{16} cos \frac{2 π}{16} \times 2 = r \times \frac{2 π}{16} \times \frac{1}{16} \times \frac{1}{2}$
or $r = \frac{0.4 \times 16 \times 2}{2 π} = \frac{3.2 2}{π} = 1.44 m$

Q. The time period of a particle undergoing SHM is 16s. It starts motion from the mean position. After 2s, its velocity is 0.4ms−1. The amplitude is