0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

The potential energy of a particle of mass 1 kg in motion along the x-axis is given by U=4(1cos2x) J. Here x is in meter. The period of small oscillations (in sec) is _______.
  1. 2π
  2. π
  3. π2
  4. 2π

A
π
B
2π
C
π2
D
2π
Solution
Verified by Toppr

M=1 kg
U=4(1cos2x)
F=dudx
F=4[0(sin2x)(2)]
F=8sin2x N
a=8sin2x m/sec2[ m=1 kg]
a8(2x)
a=16x [For small x,sinxx]
ω2=42
ω=4 rad /ac
T=2πw=π2sec

Was this answer helpful?
14
Similar Questions
Q1
The potential energy of a particle of mass 1 kg in motion along the x-axis is given by U=4(1cos2x) J. Here x is in meter. The period of small oscillations (in sec) is _______.
View Solution
Q2
The potential energy of a particle of mass 1 kg moving along the X-axis is given by U=4(1+cos2x) J, where x is in meters. Find the time period of small oscillation (in second).
View Solution
Q3
The potential energy of a particle of mass 1 kg in motion along the x axis is given by U=4(1cos 2x) J, where x is in m. The period of small oscillations (in s) is
View Solution
Q4
The potential energy of a particle of mass 1 kg moving along the X-axis is given by U=4(1+cos2x) J, where x is in meters. Find the time period of small oscillation (in second).
View Solution
Q5
A particle of mass 2 kg executes simple harmonic motion and its potential energy U varies with position x as shown below. The period of oscillation of the particle is


View Solution
Solve
Guides