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A mass $m$ is attached to a vertical spring. According to Hooke's Law and Newton's Second Law, its displacement $y(t)$ from the equilibrium position is governed by the second-order differential equation:$$m\frac{d^2 y}{dt^2} = -ky$$where $k$ is the positive spring constant. This describes Simple Harmonic Motion.

The mass is pulled down to a position of $y=-A_0$ and released from rest at $t=0$. State the initial conditions for $y(0)$ and $y'(0)$.
Verify that the general solution is $y(t) = C_1\cos(\omega t) + C_2\sin(\omega t)$, where $\omega = \sqrt{\frac{k}{m}}$ and $C_1, C_2$ are arbitrary constants.
Use the initial conditions to find the particular solution for the mass's motion.

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