A body of mass `m` is in a field where its potential energy is given by `U = ax^(3) +bx^(4)`, where `a` and `b` are positive constants. Then, [The body moves only along `x`]

Options

A. `x = 0` is a point of equilibrium
B. `x = (-3a)/(4b)` is a point of stable equilibrium
C. `x = (-3a)/(4b)` is a point of unstable equilibrium
D. for small displacements from stable equilibrium position the body executes `SHM` with angular frequency `(3a)/(2sqrt(bm))`

Answer

A, B, D

Explanation

`U = ax^(3) +bx^(4)`
`F = (delU)/(delx)= -3ax^(2) - 4bx^(3)`
`F = 0 at x = 0` and `x = (-3a)/(4b)`
For small displacement restoring force is given by,
`F_(res) = (9a^(2))/(4b) deltax`