A particle of mass 4 kg moves simple harmonically such that its PE ( U ) varies with position x, as shown. The period of oscillations is:-

Question

A particle of mass 4 kg moves simple harmonically such that its PE ( U ) varies with position x, as shown. The period of oscillations is:- (A) (2 π/25) s (B) (π √2/5) s (C) (4 π/5) s (D) (2 π √2/5) s

Tardigrade Admin · Accepted Answer

U max =(1/2) kx 2 1=(1/2) k (0.2)2 ⇒ k =50 and T =2 π √( m / k ) ⇒ T =2 π √(4/50)=(2 π √2/5) sec

Q. A particle of mass $4 k g$ moves simple harmonically such that its $PE (U)$ varies with position $x$ , as shown. The period of oscillations is:-

$\frac{2 π}{25} s$

$\frac{π 2}{5} s$

$\frac{4 π}{5} s$

$\frac{2 π 2}{5} s$

$U_{m a x} = \frac{1}{2} k x^{2}$
$1 = \frac{1}{2} k (0.2)^{2}$
$\Rightarrow k = 50$
and $T = 2 π \frac{m}{k}$
$\Rightarrow T = 2 π \frac{4}{50} = \frac{2 π 2}{5} sec$

Q. A particle of mass 4kg moves simple harmonically such that its PE(U) varies with position x, as shown. The period of oscillations is:-

252π​s

5π2​​s

54π​s

52π2​​s