A small ball of mass m is attached to two identical springs along the y-axis. The spring constants are k and relaxed lengths are Lo. When aligned along the y-axis the springs are compressed, the distance wwwwwwwwwwwwww wwwwwwwww wwwww between their respective points of attachment is 2L< 2Lo. Initially the ball is constrained to move in the x-axis. There is no gravity. www wwwwwwwwww www. a) Find the potential energy of the ball as a small displacement x for small amplitude oscillations. wwwwwwwwwwwwwww wwwwww.son Expand it as a power series up to x^4 wwwwwwww wwwwww wwww www www www A high frequency external force F = -(mXow 2) cos(wt) i is applied to the ball along the x-axis. The frequency w of the external force is much larger than the free oscillation frequency of the ball. www b) Write the equation of motion for the ball. Separate the equation into high and low frequency by appropriate substitution of variable. c) Find the effective potential Ueff for the low frequency motion of the ball by averaging U(x) over many oscillations of the external force. wwwww d) Find the equlibrium points and the frequency of small low frequency oscillations in the effective wwwwwwwwww! potential as a function of the parameter Xo wwwwwwwwwwww wwwwwwwwwww