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Repeated to-and-fro motion about a mean position.
Examples: Pendulum, mass-spring system, LC circuit.
Mass Spring System
Pendulum
LC circuit
Periodic Motion: Motion that repeats itself after a fixed time.
Time Period (T): Time taken to complete one oscillation.
Frequency (f): Number of oscillations per second
Angular Frequency (ω)
1. Restoring force should exist.
2. Restoring force ∝ displacement from mean position.
Simple Harmonic Motion or S.H.M is the special type of oscillation in which the restoring force is directly proportional to the displacement of the body from its mean position or equilibrium position.
the kinematics of Simple Harmonic Motion (SHM) involves understanding its equations for displacement, velocity, and acceleration, which are derived from the projection of uniform circular motion, and applying them to problems.
A spring-mass oscillator is a system where a mass is attached to a spring, resulting in oscillatory motion called simple harmonic motion when displaced from its equilibrium position.
A simple pendulum can be described as a device where its point mass is attached to a light inextensible string and suspended from a fixed support.
a simple pendulum involves an ideal mass (bob) suspended by a massless, inextensible string, executing simple harmonic motion (SHM) for small angles.
where,
𝑙 = the length of the pendulum
𝑔 = the acceleration due to gravity.
Key concepts include the dependence of the period on length and 'g',
but not on mass or amplitude for small oscillations.
LC oscillations are the energy exchange between a charged capacitor and an inductor in a resonant circuit (LC circuit), forming a continuous back-and-forth transfer of energy between electrical and magnetic forms.