Question #103279

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.

Expert's answer

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}}"

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