A body of mass m is situated in a potential field U(x) = U0 (1 – cos αx) when U0 and α are constants. Find the time period of small oscillations.

contexto.120

3 years ago

Answer:

According to the question, we have:

$U = U_{0} (1 - c o s α x)$

We know taht, F = - d U

As it is given that

α x

is small, so sin $α x \sim α x$

Here, F \propto x

and negative sign shows that

For SHM, we know that

$F = - k x$

Comparing equations, we get,

We can write the time period of oscillation as follows: