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SithsNGiggles
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Homework Statement
Suppose a cart of mass 2 kg is attached by a spring of constant k = 1 to a cart of mass 3 kg, which is attached to the wall by a spring also of k = 1. Suppose the initial position of the first cart is 1 m in the positive direction from the rest position, and the second mass starts at the rest position. The masses are not moving and are let go. Find the position of the second mass as a function of time.
Homework Equations
The Attempt at a Solution
It's been a while since I've taken physics, so I'm a bit lost on the setup for this system. I've attached an image of the scenario. Are my forces (green arrows/text) for each mass correct?
If this is right, then my system of equations is
##\begin{cases}
m_1x_1''=-k_1x_1+k_1x_2\\
m_2x_2''=k_1x_1 + (k_2-k_1)x_2
\end{cases}##
Plugging in the given values, it becomes
##\begin{cases}
2x_1''=-x_1+x_2\\
3x_2''=x_1
\end{cases}##
Or, as a matrix equation,
##\left(\begin{matrix}2&0\\0&3\end{matrix}\right)\vec{x}\;'' = \left(\begin{matrix}-1&1\\1&0\end{matrix}\right)\vec{x}##
Is this all right so far? I'm confident I can solve the system, but not as much about the setup. Thanks