3. A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other. Assume the two pendula have equal lengths $l$, equal masses $m$, and are confined to move in the same plane.
a. Derive the equations of motion for $\phi_1(t)$ and $\phi_2(t)$. Hint: these should be two coupled $2^{nd}$ order nonlinear differential equations.
b. If $\phi_1(t) = 0$, what is the differential equation that your equations of motion from a) reduce to? Does this equation make sense?
c. For $\phi_1(t) = 0$, what is the frequency of small oscillations?