- #1
SithsNGiggles
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Homework Statement
Take the example in Figure 3.12 on pg 117 (see attachment) with parameters ##m_1=m_2=1## and ##k_1=k_2=1##. Does there exist a set of initial conditions for which the first cart moves but the second cart does not? If so, find those conditions.
Homework Equations
The Attempt at a Solution
Here's my set-up:
##\begin{cases}
x_1'' = -2x_1+x_2\\
x_2'' = x_1-x_2
\end{cases}##
And I'm not sure whether my reasoning is valid here, but since we're trying to find conditions for which ##m_2## doesn't move, does that mean ##x_2=0##?
This would leave me with just
##x_1''=-2x_1##,
and from the second equation we get ##x_1=0## as well.
Because of this, I'm led to believe the initial conditions are something like ##x_1(0)=0## and ##x_2(0)=0##.