Key Topic 2.3: Phase and Initial Conditions

In SHM, the general solution for position is:

x(t) = A \cos(\omega t + \phi)

Given initial conditions $x_0$ and $v_0$, we can solve for $A$ and $\phi$:

A = \sqrt{x_0^2 + \left(\frac{v_0}{\omega}\right)^2}
\phi = \tan^{-1}\left(\frac{-v_0}{\omega x_0}\right)

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