The shortest distance travelled by a particle (performing S.H.M.) from mean position in 2 seconds is equal to (√3/2) of its amplitude. Find its period.

Question

The shortest distance travelled by a particle (performing S.H.M.) from mean position in 2 seconds is equal to (√3/2) of its amplitude. Find its period. (A) 11s (B) 12s (C) 13s (D) 14s

Tardigrade Admin · Accepted Answer

When t =2 s , y =(√3/2) r Now, y=r sin ω t ∴ (√3/2) r = r sin ω × 2 or sin 2 ω=(√3/2) or 2 ω=(π/3) Or ω=(π/6) Hence, T =(2 π/ω)=(2 π/π / 6)=12 s

Q. The shortest distance travelled by a particle (performing S.H.M.) from mean position in $2$ seconds is equal to $\frac{3}{2}$ of its amplitude. Find its period.

$11 s$

$12 s$

$13 s$

$14 s$

When $t = 2 s, y = \frac{3}{2} r$
Now, $y = r sin ω t$
$∴ \frac{3}{2} r = r sin ω \times 2$ or $sin 2 ω = \frac{3}{2}$
or $2 ω = \frac{π}{3}$
Or $ω = \frac{π}{6}$
Hence, $T = \frac{2 π}{ω} = \frac{2 π}{π /6} = 12 s$

Q. The shortest distance travelled by a particle (performing S.H.M.) from mean position in 2 seconds is equal to 23​​ of its amplitude. Find its period.

11s

12s

13s

14s