Physics - Simple Harmonic Motion (SHM)

Simple Harmonic Motion (SHM):

Simple Harmonic Motion (SHM) is a type of periodic motion characterized by an object oscillating back and forth around an equilibrium position.

Key Characteristics:

• Periodic Motion: Motion repeats itself at regular intervals.
• Linear Restoring Force: Force acting on the object is directly proportional to its displacement from the equilibrium position and always directed towards it.
• Simple Harmonic Oscillator: Any system exhibiting SHM, such as a mass-spring system or a pendulum.

Mathematical Representation:

• Displacement (x) of an object undergoing SHM: x(t)=A⋅sin(ωt+ϕ)
  • x(t): Displacement at time t
  • A: Amplitude (maximum displacement)
  • ω: Angular frequency
  • t: Time
  • ϕ: Phase angle (initial phase)

Important Quantities:

• Amplitude (A): Maximum displacement from the equilibrium position.
• Frequency (f): Number of oscillations per unit time (measured in hertz, Hz).
• Period (T): Time taken for one complete oscillation (measured in seconds, s).
• Angular Frequency (ω): Rate of change of phase with respect to time.

Examples of SHM:

• Oscillation of a mass-spring system.
• Motion of a simple pendulum.
• Vibrations of a guitar string.

Applications:

• SHM finds applications in physics and engineering, including oscillating systems design and wave behavior analysis.