Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

A few SHM problems

  1. A squirrel monitors the temperature of his home in Central Park, NY City, for several years. His measurements are shown above and are in this data file .

    1. What is the amplitude of the changes in temperature?
    2. What is the period of the changes in temperature?
    3. What is the angular frequency of the changes in temperature?
    4. Can you write an equation which yields temperature (F) as a function of months since the start of the study?

  2. A block of M = 5 kg sits on a frictionless floor, connected to a spring of force constant k = 100 N/m. The other end of the spring sticks into the wall. I place the block at the spring's rest position. Then, I pull it an extra distance x = 0.1 m from the wall and let go at t = 0 s. The block slides left and right, left and right, so that its position at time t is given by
    1. What is A in the equation above?
    2. What is ω in the equation above?
    3. What is the period of oscillation?
    4. What is the maximum speed of the block?

    I stop the block and again place it at the rest position of the spring. Then I pull it a larger distance from the wall, x = 0.2 m, and release it.

    1. What is the period of oscillation now?
    2. What is the maximum speed of the block now?

  3. I hang a meterstick of mass m = 150 g by a hole which is h = 40 cm from the center of the rod. The meterstick is hanging straight down towards the floor, motionless.
    1. What is the moment of inertia of the rod around this hole?
    2. What is the force of gravity on the rod?

      3. I now move the meterstick so that it hangs at angle of theta from the vertical.

    3. What is the torque on the meterstick?

      4. I release the meterstick.

    4. Write an equation which shows the angular acceleration of the meterstick.
    5. Write an equation which shows the angular acceleration of the meterstick as a function of the angular displacement.
    6. Does the meterstick undergo simple harmonic motion? Explain.
    7. What is the period of the meterstick's oscillation?

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.