The potential energy of a particle of mass 1 kg in motion along the x -axis is given by: U=4(1- cos 2 x), where x is in metres. The period of small oscillation (in sec) is

Question

The potential energy of a particle of mass 1 kg in motion along the x -axis is given by: U=4(1- cos 2 x), where x is in metres. The period of small oscillation (in sec) is (A) 2 π (B) π (C) π / 2 (D) π/4

Tardigrade Admin · Accepted Answer

F=-(d U/d x)=-8 sin 2 x For small oscillations, sin 2 x=2 x i.e., a=-16 x Since a=-x the oscillations are SH in nature. T=2 π √|(x/a)| =2 π √(1/16)=(π/2) sec

Q. The potential energy of a particle of mass $1 k g$ in motion along the $x$ -axis is given by: $U = 4 (1 - cos 2 x)$ , where $x$ is in metres. The period of small oscillation (in sec) is

$2 π$

$π$

$π /2$

$π /4$

$F = - \frac{d U}{d x} = - 8 sin 2 x$
For small oscillations,
$sin 2 x = 2 x$
i.e., $a = - 16 x$
Since $a = - x$
the oscillations are SH in nature.
$T = 2 π ∣ \frac{x}{a} ∣ = 2 π \frac{1}{16} = \frac{π}{2} sec$

Q. The potential energy of a particle of mass 1kg in motion along the x -axis is given by: U=4(1−cos2x), where x is in metres. The period of small oscillation (in sec) is

2π

π

π/2

π/4

F=−dxdU​=−8sin2x For small oscillations, sin2x=2x i.e., a=−16x Since a=−x the oscillations are SH in nature. T=2π∣ax​∣​=2π161​​=2π​sec

Q. The potential energy of a particle of mass $1 k g$ in motion along the $x$ -axis is given by: $U = 4 (1 - cos 2 x)$ , where $x$ is in metres. The period of small oscillation (in sec) is

$2 π$

$π$

$π /2$

$π /4$

$F = - \frac{d U}{d x} = - 8 sin 2 x$
For small oscillations,
$sin 2 x = 2 x$
i.e., $a = - 16 x$
Since $a = - x$
the oscillations are SH in nature.
$T = 2 π ∣ \frac{x}{a} ∣ = 2 π \frac{1}{16} = \frac{π}{2} sec$