Simple Harmonic Motion

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Simple Harmonic Motion
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Periodic Motion

• When a vibration or oscillation repeats itself
  over the same time period

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Oscillating Spring System

• Equilibrium position- where spring exerts no
  force on the mass (m)
• Natural state

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Oscillating Spring System

• Spring stretched
• Exerts a force to move it back to equilibrium

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Oscillating Spring System

• Spring compressed
• Force exerted pushing it back to equilibrium

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Restoring Force (F)

• Force exerted when away from equilibrium
• - pulls it back to equilibrium
• Directly proportional to the displacement (x)
• F - kx
• k spring constant
• Greater the value of k the more force is needed
  to stretch spring - stiffer

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• F is not constant, depends on x
• F ma
• Therefore acceleration is not constant, depends
  on x

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Question

• At what position(s) is the acceleration the
  greatest?
• Where is it the least?
• Where is velocity greatest? And least?

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Other Definitions

• Amplitude (A) point of greatest displacement
• Cycle complete oscillation
• Period (T) time for one complete oscillation
• Frequency (f) cycles per second
• T 1/f

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Example

• When a family of four people (total mass 200kg)
  steps into their 1200kg car, the springs compress
  3.0 cm. A) What is the cars spring constant?
  B) How far will the car lower if loaded with
  100kg of luggage as well?

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Example

• A .10 kg object is suspended from a spring with a
  spring constant of 10 N/m. The object is pulled
  15cm from its equilibrium position and released,
  what is its maximum acceleration and when does it
  experience this?

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Simple Harmonic Motion (SHM)

• Any vibrating system where the restoring force is
  directly proportional to the negative
  displacement
• Any object exhibiting this is called a simple
  harmonic oscillator (SHO)