Simple Harmonic Motion

Answer

Periodic motion is motion that repeats itself at equal intervals of time. The smallest interval of time after which the motion repeats is called the time period (T). Examples: 1. Motion of planets ar

Answer

Periodic Motion: Any motion that repeats after equal intervals of time (includes rotational motion like planets around sun) Oscillatory Motion: To and fro motion about a mean position (like pendulum,

Answer

Simple Harmonic Motion: A particle executes SHM if its acceleration is directly proportional to its displacement from mean position and is always directed towards the mean position. Mathematical Cond

Answer

Differential Equation of SHM: d²x/dt² + ω²x = 0 General Solutions: x(t) = A sin(ωt + φ) or x(t) = A cos(ωt + φ) Where: - A = amplitude - ω = angular frequency - φ = initial phase - t = time

Answer

Amplitude (A): Maximum displacement from mean position (units: m) Time Period (T): Time taken to complete one oscillation (units: s) T = 2π/ω Frequency (f): Number of oscillations per second (units:

Answer

Given: x(t) = A sin(ωt + φ) Velocity: v = dx/dt = d/dt[A sin(ωt + φ)] v = Aω cos(ωt + φ) Maximum velocity: vₘₐₓ = Aω (at mean position) Acceleration: a = dv/dt = d/dt[Aω cos(ωt + φ)] a = -Aω² sin(ω

Answer

SHM can be represented as the projection of uniform circular motion on a diameter. Consider a particle moving in a circle of radius A with angular velocity ω: - Position: y = A sin(ωt) - The projecti

Answer

For horizontal spring-mass system: Restoring force: F = -kx (Hooke's law) From Newton's second law: F = ma Therefore: ma = -kx a = -(k/m)x Comparing with a = -ω²x: ω² = k/m ω = √(k/m) Time period: