Consider a mass m constrained to move on the x axis and

QUESTION:

Consider a mass m constrained to move on the x axis and subject to a net force \(F=-k x\) where k is a positive constant. The mass is released from rest at \(x=x_{0}\) at time t = 0. Use the result (2.85) in Problem 2.12 to find the mass's speed as a function of x; that is, dx/dt = g(x) for some function g(x). Separate this as dx/g(x) = dt and integrate from time 0 to t to find x as a function of t. (You may recognize this as one way — not the easiest — to solve the simple harmonic oscillator.)