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Applying F = ma in the x-direction, we get the following differential equation for the location x(t) of the center of the mass:

Latex
Wiki Markup
{latex}
\[
m \ddot{x} + k x =0
\]
{latex}

The initial conditions at t=0 are

Latex
Wiki Markup
{latex}
\[
x(0)=1,
\]
{latex}
and

Latex
Wiki Markup
{latex}
\[
v(0)=\dot{x} ̇(0)=0
\]
{latex}

The first condition above specifies the initial location x(0) and the second condition, the initial velocity v(0).

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