Oscillations Formulas

Flashcards of key vocabulary and formulas related to oscillations as presented in the lecture notes.

Oscillation Formula 1 (Hooke's Law)

F = -kx

Oscillation Formula 2 (Newton's Second Law)

a = f/m

Oscillation Formula 3 (Angular Frequency)

w = √k/m

Oscillation Formula 4 (Acceleration in SHM)

a = -w²x

Oscillation Formula 5 (Differential Equation of SHM)

d²x/dt² + w²x = 0

Oscillation Formula 6 (Velocity in SHM)

v = ± w √(A² - x²)

Oscillation Formula 8 (Displacement in SHM, sine form)

x = ± A sin(wt + φ) - (mean position)

Oscillation Formula 8ii (Displacement in SHM, cosine form)

x = ± A cos(wt) - (Extreme position)

Oscillation Formula 9 (Velocity and position relationship)

Vmin = 0 ; xmax = ± A

Oscillation Formula 10 (Acceleration limits)

amin = 0 ; amax = ± w²A

Oscillation Formula 11 (Amplitude Condition)

sin(wt + φ) = ± 1 (Amplitude)

Oscillation Formula 12 (Period of SHM)

T = 2π √(m/k)

Oscillation Formula 13 (Frequency of SHM)

n = 1/(2π) √(k/m)

Oscillation Formula 14 (Velocity when starting from mean position)

v = Aw cos(wt + φ), particle starts from mean position

Oscillation Formula 15 (Acceleration when starting from mean position)

a = -Aw² sin(wt + φ)

Oscillation Formula 16 (Displacement as a function of time)

y = A sin(wt + φ), (θ = wt + φ)

Oscillation Formula 17 (Displacement with cosine)

x = A cos wt

Oscillation Formula 18 (Velocity with sine)

V = -Aω sin ωt

Oscillation Formula 19 (Acceleration with cosine)

a = -Aω² cos ωt

Oscillation Formula 20 (Kinematic Equation)

R sin(ωt + δ)

Oscillation Formula 21 (Resultant Amplitude)

√(A₁² + A₂² + 2A₁A₂ cos(θ₁ - θ₂))

Oscillation Formula 22 (Phase angle of Resultant)

tan⁻¹((A₁ sin θ₁ + A₂ sin θ₂) / (A₁ cos θ₁ + A₂ cos θ₂))

Oscillation Formula 23 (Maximum Amplitude)

A₁ + A₂ (θ₁ - θ₂ = 0)

Oscillation Formula 24 (Amplitude at right angles)

√(A₁² + A₂²) (θ₁ - θ₂ = π/2)

Oscillation Formula 25 (Minimum Amplitude)

A₁ - A₂ (θ₁ - θ₂ = π)

Oscillation Formula 26 (Kinetic Energy)

1/2 k (A² - x²)

Oscillation Formula 27 (Potential Energy)

1/2 kx²

Oscillation Formula 28 (Total Energy)

1/2 kA²

Oscillation Formula 29 (Kinetic Energy At mean position)

1/2 kA²

Oscillation Formula 30 (Potential Energy At mean position)

0

Oscillation Formula 31 (Kinetic Energy At extreme position)

0

Oscillation Formula 32 (Potential Energy At extreme position)

1/4 kA²

Oscillation Formula 33 (Displacement for half energy)

A/√2

Oscillation Formula 34 (Position for half energy)

x = ± A/2

Oscillation Formula 35 (Simple Pendulum Period)

2π √(l/g)

Oscillation Formula 36 (Simple Pendulum Angular Frequency)

√(g/l)

Oscillation Formula 37 (Simple Pendulum Frequency Factor)

√(l/g)

Oscillation Formula 38 (Force)

ma

Oscillation Formula 39 (Torque)

Iα

Oscillation Formula 40 (Moment of Inertia)

MR²

Oscillation Formula 41 (Restoring Torque)

-Cθ

Oscillation Formula 42 (Angular Acceleration)

-ω²θ

Oscillation Formula 43 (Torsional SHM Differential Equation)

d²θ/dt² + ω²θ = 0

Oscillation Formula 44 (Torsional SHM Angular Frequency)

√(C/I)

Oscillation Formula 45 (Magnetic SHM Torque)

4πB sinθ

Oscillation Formula 46 (Magnetic Moment)

mx 2l -> Magnetic length

Oscillation Formula 47 (Magnetic SHM Equation)

d²θ/dt² + μBθ = 0

Oscillation Formula 48 (Magnetic SHM Period)

2π √(I/μB)

Oscillation Formula 49 (Magnetic SHM Angular Acceleration)

(μ/I) θ

Oscillation Formula 50 (Damped Oscillation Equation)

m d²x/dt² + b dx/dt + kx = 0

squared angular frequency (Formula name)

k/m - (b/2m)²

Oscillation Formula 51 (Damped Oscillation Solution)

Ae ^(-bt/2m) cos(ω't + φ)

Oscillation Formula 5

√(k/m - (b/m)^2)