Question

4) A body of mabb M is situated in a potar tial field u(x) = Mo (1-Cobelan), where Constants. The time perioud of small obcillations of body will be to and I are​

Answer 1

U =U0(1-cosαx)

F = -dU/dx

F = -d/dx[U0(1-cosαx)] =U0​αsinαx

As αx is small,so sin αx∼αx

∴F=−U0​α2x     ...(i)

F∝x and −ve shows that F is directed towards the mean position, hence the body executes SHM.

For SHM, F=−kx

Comparing (i) and (ii), we get, k=U0​α2

Time period of oscillation,

T=2πkm​√m/k

 = 2π√m/U0​α2m​

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Answer 2

Answer:

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