Simple Harmonic Motion

A particle executes SHM when its

A particle executes SHM when its acceleration is directly proportional to displacement from equilibrium position and directed towards equilibrium posi

Displacement

Displacement: x(t) = A sin(ωt + φ), Velocity: v(t) = Aω cos(ωt + φ), Acceleration: a(t) = -Aω² sin(ωt + φ). Where A is amplitude, ω is angular frequen

Spring

Spring-mass system: T = 2π√(m/k), Simple pendulum: T = 2π√(l/g). These are derived from the condition that restoring force is proportional to displace

Kinetic Energy

Kinetic Energy: KE = ½mω²(A² - x²), Potential Energy: PE = ½mω²x², Total Energy: E = ½mω²A² = ½kA² (constant). Energy continuously transforms between

SHM can be represented as

SHM can be represented as the projection of uniform circular motion on a diameter. A particle moving in a circle of radius A with angular velocity ω h