A particle of mass `m` moving along x-axis has a potential energy `U(x)=a+bx^2` where a and b are positive constant. It will execute simple harmonic motion with a frequency determined by the value of

Options

A. b alone
B. b and a alone
C. b and m alone
D. b,a and m alone

Answer

C

Explanation

`U=a+bx^2`
`F=-(dU)/(dx)=-[0+2bx]`
`F=ma=-2bximpliesa=-((2b)/(m))x`
`omega=2pif=((2b)/(m))^((1)/(2))`
Hence frequency depends upon b and m