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# Rotational Simple Harmonic Oscillation: Rod with two springs

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A 1-dimensional rod 2 meters long of mass 60 grams uniformly distributed has an axle through its midpoint allowing the rod to rotate in a vertical plane. At each end of the rod are identical, ideal springs which have spring constants of 40 N/cm. At equilibrium the rod lies horizontally in the vertical plane. The rod is given a slight rotational displacement of 5° about the axle through its center and then released. Assume the displacement is small enough such that the springs essentially stretch/compress in the vertical direction only and that the small-angle approximation can be used.

Determine the following:

a.) the angular frequency of the oscillation
b.) the period of the oscillation
c.) the kinetic energy of the rod 2 seconds after it is released
d.) the angle the rod is displaced from equilibrium 2 seconds after it is released

##### Solution Summary

A rod attached with two springs can rotate about midpoint. The angular frequency, period of oscillation, and position with time is calculated.

##### Solution Preview

A 1-dimensional rod 2 meters long of mass 60 grams uniformly distributed has an axle through its midpoint allowing the rod to rotate in a vertical plane. At each end of the rod are identical, ideal springs which have spring constants of 40 N/cm. At equilibrium the rod lies horizontally in the vertical plane. The rod is given a slight rotational displacement of 5° about the axle through its center and then released. Assume the displacement is small enough such that the springs essentially stretch/compress in the vertical direction only and that the small-angle ...

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