Question

the potential energy of a particle of mass 1 kg along x-axis is U=5(1-cos3x).time period will be??​

Answer 1

Answer:

Explanation:-

Answer 2

The time period of small oscillation is 2π/3√5

Given-

• Mass of the particle = 1 kg
• Potential energy along x axis = 5 (1 - cos 3x) J

We know that there is a relation between force and potential energy and that is

F = - dU/dx

U = -∫F. dx

So,

F = - d [5(1-cos 3x)] / dx

F = -15 sin 3x

F = -15 × 3x

For small oscillations we can write sinФ = Ф. So,

F = -45x

ma = -45x

a = -45x

We know that acceleration (a) = -ω²x

By comparing we get ω² = 45

ω = √45

And we know that ω = 2π/T

2π/T = √45

T = 2π/3√5