Lesson 11: Simple Harmonic Motion

Write your solutions to the following problems and submit them before 6 am on Wednesday, April 2nd.

Submit to the SUBMIT folder on Priscilla or as an attachment to an e-mail message to rfuller@unlinfo.unl.edu or using this Web form.

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  1. A body of mass 0.25 kg is acted on by an elastic restoring force of force constant k = 25 N/m.

    1. Construct the graph of the elastic potential energy U as a fuction of displacement x, over a range of x from -0.3 m to +0.3 m.

      If the body is set into oscillation with an initial potential energy of 0.6 J and an initial kinetic energy of 0.2 J, answer the following questions by reference to the graph:

    2. What is the amplitude of oscillation?

    3. What is the potential energy when the displacement is one-half the amplitude?

    4. At what displacement are the kinetic and potential energies equal?

    5. What is the speed of the body at the midpoint of its path?

      Find the following:

    6. The period.

    7. The frequency.

    8. The angular frequency.

  2. A body of mass m is suspended from a coil spring and the time for 100 complete oscillations is measured for the following values of m:

    m (g) Time for 100
    oscillations (s)
    100 23.4
    200 30.6
    400 41.8
    1000 64.7

    1. Plot graphs of the measured values of T vs. m, and T2 vs. m where T is the period of oscillation.

    2. Are the experimental results in agreement with theory?

    3. Is either graph a straight line?

    4. Does the straight line pass through the origin?

    5. What is the force constant of the spring?

    6. What is the mass of the spring?

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