Introduction to Simple Harmonic Motion

Physics

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Time-period from equation of SHM

Equation of SHM:
Angular frequency
Frequency
Time-period
Example:
Acceleration-displacement graph of a particle executing SHM is as shown in the figure. Find the time period of oscillation.
Solution:
In SHM

or

so, from graph
                 

Time period


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Simple Harmonic Motion

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Applications of SHM

Some applications of SHM are:
  • Simple harmonic motion of a pendulum is used for the measurement of time.
  • Tuning of the musical instrument is done with the vibrating tuning fork which executes simple harmonic motion.
  • Wave is a consequence of simple harmonic motion. Study of waves is indirectly the study of simple harmonic motion.
  • Molecules are in simple harmonic motion. This study is called vibration spectroscopy.

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Characteristics of SHM

  1. A restoring force must act on the body.
  2. Body must have acceleration in a direction opposite to the displacement and the acceleration must be directly proportional to displacement.
  3. The system must have inertia (mass).
  4. SHM is a type of oscillatory motion.
  5. It is a particular case of preodic motion.
  6. It can be represented by a simple sine or cosine function
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