A particle of mass m undergoes oscillation about x = 0 in a potential energy given by V ( x ) = V 0 cos ( a x ) where V 0 and a are constant. If the amplitude of oscillation is much smaller than

Question

A particle of mass m undergoes oscillation about x = 0 in a potential energy given by V ( x ) = V 0 ​ cos ( a x ​ ) where V 0 ​ and a are constant. If the amplitude of oscillation is much smaller than a , the time period is given by

TestHub · Accepted Answer

F = − d x d V ​ = a V 0 ​ ​ sin a x ​ For small oscillations sin a x ​ ≈ a x ​ , so F ≈ a 2 V 0 ​ ​ x , an SHM with k = a 2 V 0 ​ ​ . T=2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{ma^2}{V_0}}} Answer: C

Physics - SHM Question with Solution | TestHub

Options:

Doubts & Discussion