A body of mass m is situated in a potential field when
and
are constants. Find the time period of small oscillations.
Here, dW = F.dx
So, if W = U, dU = F.dx
Or ….. (since, restoring force here is opposite to displacement)
Now, is small for SHM, So sin
will become
…… (i)
Thus,
Now, since, &
are constants,
Thus, the motion will be SHM.
From (ii)
Thus,
Thus, considering (i) time period is valid for the small-angle .