Oscillations — Formula Sheet
Maharashtra Board · Class 12 · Physics
11 formulas from Oscillations (Maharashtra Board Class 12 Physics) on one page, grouped by topic. Part of the Maharashtra Board Class 12 Physics syllabus.
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Formulas and Key Relations
Simple Harmonic Motion (SHM)
Acceleration
a = -ω²x (proportional to displacement, opposite in direction)
Energy in Simple Harmonic Motion
Kinetic energy
KE = ½mv² = ½mω²(A² - x²)
Potential energy
PE = ½kx² = ½mω²x²
Simple Pendulum
Restoring force
F = -mg sin θ ≈ -mgθ (for small θ)
Time period
T = 2π√(L/g) - independent of mass and amplitude
Key relations
d²x/dt² + ω²x = 0, derived from F = -kx and Newton's second law.
Solution gives x = A sin(ωt + φ), v = Aω cos(ωt + φ), a = -Aω² sin(ωt + φ).
Total energy E = KE + PE = ½mω²A² remains constant.
At mean position
KE = maximum, PE = 0.
At extreme positions
KE = 0, PE = maximum.
Rotational oscillations where restoring torque τ = -cθ is proportional to angular displacement.
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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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