Oscillations – Meaning, Types, and Formulas

What are Oscillations?

Oscillations are repeated back-and-forth movements of an object around a fixed position.

In simple words – It’s when something moves to and fro in a regular way .

Example:

• A swinging pendulum.
• A vibrating guitar string.
• A mass hanging from a spring.

Important Terms:

Mean Position (Equilibrium Position):
The position where the object stays at rest when no force is applied.

1. Amplitude (A):
   The maximum displacement from the mean position.
2. Time Period (T):
   Time taken for one complete oscillation.

3. Frequency (f):
   Number of oscillations per second.

   
4. Phase:
   Describes the position and direction of motion at a given instant.

Simple Harmonic Motion (SHM):

A special type of oscillation where:

• The restoring force is directly proportional to displacement.
• Direction of restoring force is opposite to displacement.

Equation of SHM:

Where:

• FFF = restoring force
• kkk = force constant
• xxx = displacement

Formulas:

• For a mass-spring system:

  

• For a simple pendulum:

  

  Where:

  • lll = length of pendulum
  • ggg = acceleration due to gravity

Daily Life Examples:

• Swing in a park.
• Shock absorbers in vehicles.
• Tuning forks in musical instruments.

Summary:

Oscillations are to-and-fro motions about a fixed position. SHM is the simplest form of oscillation, with force proportional to displacement and opposite in direction.