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`]

A particle of mass m is moving in a potential well, for which the potential energy is given by U(x) = U_(0)(1-cosax) where U_(0) and a are positive constants. Then (for the small value of x)

A particle of mass m is moving in a potential well, for which the potential energy is given by U(x) = U_(0)(1-cosax) where U_(0) and a are positive constants. Then (for the small value of x)

The potential energy of a conservative is given by u = ax^2 - bx , where a and b are positive constants. Discuss whether the equilibrium is stable, Unstable or neutral.

A particle of mass m moves in a one dimensional potential energy U(x)=-ax^2+bx^4 , where a and b are positive constant. The angular frequency of small oscillation about the minima of the potential energy is equal to