Explore BrainMass

Explore BrainMass

    Rotational Simple Harmonic Oscillation: Rod with two springs

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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

    © BrainMass Inc. brainmass.com December 15, 2022, 7:24 pm ad1c9bdddf
    https://brainmass.com/physics/torques/rotational-simple-harmonic-oscillation-rod-two-springs-218296

    Attachments

    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 ...

    Solution Summary

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

    $2.49

    ADVERTISEMENT