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# A mass is placed on a frictionless, horizontal table. A spring $(k=100 \mathrm{~N} / \mathrm{m})$, which can be stretched or compressed, is placed on the table. A $5.00-\mathrm{kg}$ mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zéro. A student moves the mass out to $x=4.0 \mathrm{~cm}$ and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion. (b) Find the position, velocity, and acceleration of the mass at time $t=3.00 \mathrm{~s}$.

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a) The equation of motion is derived from Newton's second law.

\begin{align*} F &= ma \\ -kx &= m\ddot{x} \\ \ddot{x} + \omega^2x &= 0 \end{align*}

Where we used a supstitution $\omega^2 = \dfrac{k}{m}$

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