Answer to Question #102686 in Mechanics | Relativity for sakshi

Question #102686
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.
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Expert's answer
2020-02-24T10:58:19-0500

Normal mode frequencies can be calculated by the following two equations:


ω1=gL, ω2=m1m2g+kL(m1+m2)m1m2L.\omega_1=\sqrt{\frac{g}{L}},\\ \space\\ \omega_2=\sqrt{\frac{m_1m_2g+kL(m_1+m_2)}{m_1m_2L}}.

The diagram corresponding to the first mode:




The diagram corresponding to the second mode:


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