Purchase Solution

Rotational Simple Harmonic Oscillation: Rod with two springs

Not what you're looking for?

Ask Custom Question

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

Attachments
Purchase this Solution

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

Please see the attachment.

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 ...

Purchase this Solution


Free BrainMass Quizzes
Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

The Moon

Test your knowledge of moon phases and movement.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

Basic Physics

This quiz will test your knowledge about basic Physics.