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

SHM in action

I have a spring of rest length Lo. It hangs motionless from a horizontal rod. When I hang a block of mass M from the spring, the spring grows longer by Δ L.

  1. Write an equation which shows all the forces on the block in the vertical direction.
  2. What is the spring constant k of this spring?

    3. Now, I grab the block and lift it up a small distance y from the equilibrium position. I then release it at time t = 0.

  3. Write an equation which shows all the forces on the block in the vertical direction.
  4. Write Newton's Second Law for the block.
  5. Solve for the acceleration of the block in the vertical direction.

  6. Solve the differential equation, to find a function which yields the y-position of the block as a function of time in the following form:

  7. What are the values of these parameters? Include the units!

  8. Predict the time it should take for the block to make one full cycle of oscillation after I release it.

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