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

Question

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

Tardigrade Admin · Accepted Answer

Velocity, v=rω cos ω t; 0.4=r× (2 π /16)cos (2 π /16)× 2=r× (2 π /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 Simple Harmonic motion 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, $v = r ω cos ω t;$
$0.4 = r \times \frac{2 π}{16} cos \frac{2 π}{16} \times 2 = r \times \frac{2 π}{16} \times \frac{1}{2}$
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 Simple Harmonic motion is 16s . It starts motion from the mean position. After 2s , its velocity is 0.4ms−1 . The amplitude is

1.44m

0.72m

2.88m

0.36m