Chapter 4, Problem 48CR

(a)

To determine

The solution of equations ${\theta }_1{}^{\prime \text{}\prime }+\frac{g}{l}{\theta }_1=-\frac{k}{m}\left({\theta }_1-{\theta }_2\right)$ and ${\theta }_2{}^{\prime \text{}\prime }+\frac{g}{l}{\theta }_2=\frac{k}{m}\left({\theta }_1-{\theta }_2\right)$ using Laplace transform when ${\theta }_1\left(0\right)={\theta }_0$, ${\theta }_1{}^{\prime }\left(0\right)=0$, ${\theta }_2\left(0\right)={\psi }_0$ and ${\theta }_2{}^{\prime }\left(0\right)=0$.

(b)

To determine

The motion of the coupled pendulum in special cases using the obtained solution in subpart (a).