Sound WavesHard
Question
A particle of mass is executing oscillations about the orgin on the x-axis. Its potential energy is V(x) = k |x|3 , where k is a positive constant. if the amplitude of oscillation is a, Then its time period T is
Options
A.proportional to 
B.proportional to √a
C.independent a3/2
D.none of these
Solution
V(x) = k |x|3
since, F = -
= - 3k|x| 2 ....(1)
X = a sin (ωt)
This equation always fits to the differential equation
= - ω2x or m 
= - mω2x
⇒ f = - mω2x ....(2)
Equation(1)and(2)give
- 3k|x|2 = - mω2x
⇒ ω =
[sin(ωt)]1/2
⇒ ω ∝ √a ⇒ T ∝
since, F = -
= - 3k|x| 2 ....(1)X = a sin (ωt)
This equation always fits to the differential equation
= - ω2x or m = - mω2x ⇒ f = - mω2x ....(2)
Equation(1)and(2)give
- 3k|x|2 = - mω2x
⇒ ω =
[sin(ωt)]1/2⇒ ω ∝ √a ⇒ T ∝
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