Simple Harmonic Motion and Circular Motion

Simple harmonic motion is closely related to a uniform circular motion.

A real life simple harmonic motion.

Review Question 1

Answer the following questions as you watch the first YouTube video(Simple harmonic motion and uniform circular motion).

  1. How does the centre of the red cylinder and the green ball relate?
  2. At which part of the SHM(left) is the red cylinder moving the fastest and slowest?
  3. At which part of the circular motion(right) is the green ball moving vertically the fastest and slowest?

Review Question 2

Navigate to this site. This animation shows how a 4-stroke engine internal combustion works.

Answer the following questions:

piston

  1. The piston is moving with SHM. At which point is the piston the fastest?
  2. At which point is the piston moving the slowest?

piston2

Given that the maximum velocity of the piston is v,

  1. write down the expression of the velocity of the piston at the position shown in the diagram.
  2. write down the expression of the acceleration of the piston at the position shown in the diagram.
  3. Sketch a velocity-time graph of the SHM demonstrated by the piston. Draw two complete cycles and label the parts A, B and C on your graph.
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