# For a certain oscillator the n

For a certain oscillator the net force on the body with mass m is given by F. = -ex.
(a) What is the potential energy function for this oscillator if we take U = 0 at x = O?
(b) One-quarter of a period is the time for the body to move from x = 0 to x = A. Calculate this time and hence the period. [Hint: Begin with Eq. (13.20), modified to include the potential-energy function you found in part (a), and solve for the velocity v. as a function of x. Then replace v, with dx/dt. Separate the variable by writing all factors containing x on one side and all factors containing t on the other side so that each side can be integrated. In the x-integral make the change of variable u = X/A. The resulting integral can be evaluated by numerical methods on a computer and has the value Jdu/~ = 1.31.J
(c) According to the result you obtained in part (b), does the period depend on the amplitude A of the motion? Are the oscillations simple harmonic?

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