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Oscillations and Simple Harmonic Motion - Coggle Diagram
Oscillations and Simple Harmonic Motion
Concept
Oscillatory Motion (Moving repetitively about the equilibrium)
Period, T is time taken for 1 complete oscillation
Frequency, f is oscillations completed in one second
Angular frequency, ω is rate of change of angle over time
Equations
x(t) = A cos ( ωt + ∅ )
v(t) = - A ω sin ( ωt + ∅ )
a(t) = - A ω² cos ( ωt + ∅ )
Energy in SHM
Potential Energy = ½kx²
Kinetic Energy = ½mv²
Total Energy = ½kA²
ω = 2πf
T=1/f
ω² = k/m
T = 2π√(k/m)
k=2π/λ
Pendulum
Restoring Force = -mg sin θ
T = 2π√(l/g)
Damped Oscillations
Damping Force = -bv
-m(d²x/dt²)+b(dx/dt)+kx=0
x(t) = A e^(-bt) cos (ω't + ∅)
β=b/2m
ω'=√(ω₀²⁻β²)