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A particle of mass (m) is executing osci...

A particle of mass (m) is executing oscillations about the origin 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.

A

proportional to `(1)/(sqrta)`

B

independent of a

C

proportional to `sqrta`

D

proportaional to `a^(3//2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`u=k|x|^(3)`
`U_("max")=ka^(3)`
The oscillation energy is given by `(1)/(2)ma^(2)omega^(2)`.
`therefore" "(1)/(2)ma^(2)omega^(2)=ka^(2)a`
or `omega^(2)=(2k)/(m)a`
or `omega=sqrt([((2k)/(m))a])`
`therefore" "T=(2pi)/(omega)=2pisqrt((m)/(2ka))`
`therefore" "Tprop(1)/(sqrta)`
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