# Two pendula of equal lengths and equal masses are coupled together by a spring with spring constant k

Sigchi4life
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Two pendula of equal lengths and equal masses are coupled together by a spring with spring constant k, as shown in Figure 6.20. The spring is unstretched when both pendula are hanging vertically in their equilibrium positions. Assume small angle motion throughout and that the motion is in the plane.

a. Find the natural frequencies of oscillation and the normal modes of the system.

b. For arbitrary, but small, initial angles and angular velocities, ﬁnd the equations of motion for the two pendula.

c. Suppose the left pendulum is released from rest with an angle , while the other is motionless and vertical. How long will it take before the right pendulum is moving and the left pendulum is at rest at θ1 =0?

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