In Problem 40, solve the same equation of motion, except with \(F_{1}(t)=\cos (2 \sqrt{k / m} t)\) and \(F_{2}(t)=0\). Plot the displacement time histories.

Problem 40:

Solve Example 6.14 with the equation of motion
\[
\begin{gathered}
{\left[\begin{array}{cc}
m & 0 \\
0 & m
\end{array}\right]\left\{\begin{array}{c}
\ddot{x}_{1} \\
\ddot{x}_{2}
\end{array}\right\}+\left[\begin{array}{cc}
3 k & -2 k \\
-2 k & 2 k
\end{array}\right]\left\{\begin{array}{l}
x_{1} \\
x_{2}
\end{array}\right\}} \\
=\left\{\begin{array}{c}
F_{1}(t) \\
F_{2}(t)
\end{array}\right\}
\end{gathered}
\]
for \(F_{1}(t)=\cos (0.66 \sqrt{k / m} t)\) and \(F_{2}(t)=0\). Plot the displacement time histories.

Example 6.14 Forced Vibration Modal Analysis Using modal analysis solve for the displacements in the two degree-of-freedom system without damping, shown in Figure 6.40.