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**[SOLVED] Simple Harmonic Oscillator**

**1. Homework Statement**

The equation of motion of a simple harmonic oscillator is (second derivative of x wrt t) d2x/dt2 = -9x, where x is displacement and t is time. The period of oscillation is?

**2. Homework Equations**

2 pi f = omega

f = 1/T

**3. The Attempt at a Solution**

Given the relevant equations, one can show that

omega / 2pi = f

2pi/omega = T

The answer is 2pi/3 by the way, and I have trouble getting to this number. I probably have to integrate something, but I don't know what that would buy me. dx/dt = -9/2 x^2 and x = -3/2 x^3. When x is sinusoidal, I know the general form of the equation, but I am totally lost here.