The potential energy of a particle of mass 2 kg in motion along the x-axis is given by U=2(1-c o s 2 x) J, where x is in meters. The period of small oscillations (in s ) is

Question

The potential energy of a particle of mass 2 kg in motion along the x-axis is given by U=2(1-c o s 2 x) J, where x is in meters. The period of small oscillations (in s ) is (A) (π/2) (B) (π/4) (C) π (D) (2 π/3)

Tardigrade Admin · Accepted Answer

U=2(1- cos 2 x) F=-(d U/d x) F=-(d/d x)(2(1- cos 2 x)) F=-4 sin 2 x For small value of x sin 2 x=2 x F=-8 x ; a=-4 x ω=2 T=(2 π/ω) =π S

Q. The potential energy of a particle of mass $2 k g$ in motion along the $x$ -axis is given by $U = 2 (1 - cos$ $2 x) J$ , where $x$ is in meters. The period of small oscillations (in $s$ ) is

$\frac{π}{2}$

$\frac{π}{4}$

$π$

$\frac{2 π}{3}$

$U = 2 (1 - cos 2 x)$
$F = - \frac{d U}{d x}$
$F = - \frac{d}{d x} (2 (1 - cos 2 x))$
$F = - 4 sin 2 x$
For small value of $x$
$sin 2 x = 2 x$
$F = - 8 x; a = - 4 x$
$ω = 2$
$T = \frac{2 π}{ω}$
$= π S$

Q. The potential energy of a particle of mass 2kg in motion along the x-axis is given by U=2(1−cos 2x)J, where x is in meters. The period of small oscillations (in s ) is

2π​

4π​

π

32π​

U=2(1−cos2x) F=−dxdU​ F=−dxd​(2(1−cos2x)) F=−4sin2x For small value of x sin2x=2x F=−8x;a=−4x ω=2 T=ω2π​ =πS

Q. The potential energy of a particle of mass $2 k g$ in motion along the $x$ -axis is given by $U = 2 (1 - cos$ $2 x) J$ , where $x$ is in meters. The period of small oscillations (in $s$ ) is

$\frac{π}{2}$

$\frac{π}{4}$

$π$

$\frac{2 π}{3}$

$U = 2 (1 - cos 2 x)$
$F = - \frac{d U}{d x}$
$F = - \frac{d}{d x} (2 (1 - cos 2 x))$
$F = - 4 sin 2 x$
For small value of $x$
$sin 2 x = 2 x$
$F = - 8 x; a = - 4 x$
$ω = 2$
$T = \frac{2 π}{ω}$
$= π S$