Question

Consider two simple pendulums P and Q of equal length L and masses m1 and m2 respectively. Suppose the bobs of the pendulum are connected to each other by a weightless spring of force constant k such that in the equilibrium position, the spring is unstretched. Calculate the normal mode frequencies, and draw labelled diagrams corresponding to each mode.

Answer 1

In short,

the first mode of oscillation

$\omega_1=\sqrt{\frac{g}{L}}$

the second mode of oscillation

$\omega_2=\sqrt{\frac{g}{L}+k\cdot \frac{m_1+m_2}{m_1\cdot m_2}}$