A particle of mass m moves in one-dimensional motion with the following potential energy f...

A particle of mass m moves in one-dimensional motion with the following potential energy functions:

(a)

(b) v(x)=kxe–bx

(c) V(x) = k(x4 – b2x2)

where all constants are real and positive. Find the equilibrium positions for each case and determine their stability.

(d) Find the angular frequency ω for small oscillations about the respective positions of stable equilibrium for parts (a), (b), and (c), and find die period in seconds for each case if m = 1 g, and k and b are each of unit value in cgs units.