The acceleration of a particle performing SHM is 12 cm / s 2 at a distance of 3 cm from the mean position. Its time period is

Question

The acceleration of a particle performing SHM is 12 cm / s 2 at a distance of 3 cm from the mean position. Its time period is (A) 0.5 s (B) 1.0 s (C) 2.0 s (D) 3.14 s

Tardigrade Admin · Accepted Answer

Acceleration a=ω2 y a =((2 π/T))2 y ⇒ T2 =(4 π2 y/a) ⇒ T=2 π √(y/a) =2 π √(3/12) T =2 π × (1/2)=3.14 s

Q. The acceleration of a particle performing SHM is $12 c m / s^{2}$ at a distance of $3 c m$ from the mean position. Its time period is

0.5 s

1.0 s

2.0 s

3.14 s

Acceleration $a = ω^{2} y$
$a = (\frac{2 π}{T})^{2} y$
$\Rightarrow T^{2} = \frac{4 π ^{2} y}{a}$
$\Rightarrow T = 2 π \frac{y}{a}$
$= 2 π \frac{3}{12}$
$T = 2 π \times \frac{1}{2} = 3.14 s$

Q. The acceleration of a particle performing SHM is 12cm/s2 at a distance of 3cm from the mean position. Its time period is