The potential energy of a particle of mass 4 kg in motion along the x-axis is given by U=4(1- cos 4 x) J. The time period of the particle for small oscillation ( sin θ=θ) is ((π/K)) s. The value of K is

Question

The potential energy of a particle of mass 4 kg in motion along the x-axis is given by U=4(1- cos 4 x) J. The time period of the particle for small oscillation ( sin θ=θ) is ((π/K)) s. The value of K is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

U =4(1- cos 4 x ) F =-( dU / dx )=-4(+ sin 4 x ) 4=-16 sin (4 x ) text For small θ sin θ ≈ θ F =-64 x a =-64 x / m =-16 x ω2=16 T =(2 π/ω)=(π/2)

Q. The potential energy of a particle of mass $4 k g$ in motion along the $x$ -axis is given by $U = 4 (1 - cos 4 x) J$ . The time period of the particle for small oscillation $(sin θ = θ)$ is $(\frac{π}{K})$ s. The value of $K$ is

$U = 4 (1 - cos 4 x)$
$F = - \frac{d U}{d x} = - 4 (+ sin 4 x) 4 = - 16 sin (4 x)$
$For small θ$
$sin θ \approx θ$
$F = - 64 x$
$a = - 64 x / m = - 16 x$
$ω^{2} = 16$
$T = \frac{2 π}{ω} = \frac{π}{2}$

Q. The potential energy of a particle of mass 4kg in motion along the x-axis is given by U=4(1−cos4x)J. The time period of the particle for small oscillation (sinθ=θ) is (Kπ​) s. The value of K is

U=4(1−cos4x) F=−dxdU​=−4(+sin4x)4=−16sin(4x) For small θ sinθ≈θ F=−64x a=−64x/m=−16x ω2=16 T=ω2π​=2π​

Q. The potential energy of a particle of mass $4 k g$ in motion along the $x$ -axis is given by $U = 4 (1 - cos 4 x) J$ . The time period of the particle for small oscillation $(sin θ = θ)$ is $(\frac{π}{K})$ s. The value of $K$ is

$U = 4 (1 - cos 4 x)$
$F = - \frac{d U}{d x} = - 4 (+ sin 4 x) 4 = - 16 sin (4 x)$
$For small θ$
$sin θ \approx θ$
$F = - 64 x$
$a = - 64 x / m = - 16 x$
$ω^{2} = 16$
$T = \frac{2 π}{ω} = \frac{π}{2}$