Oscillations Revision Notes for NEET Physics PDF Download
🌀 OSCILLATIONS · Simple Harmonic Motion
SHM • Equations • Energy • Spring-block • Pendulum • Damped & Forced • NEET problems
📐 SIMPLE HARMONIC MOTION (SHM)
Motion where restoring force is proportional to displacement and opposite in direction: F = –kx ⇒ a = –ω²x
Differential equation: d²x/dt² + ω²x = 0
Solution: x = A sin(ωt + φ) or x = A cos(ωt + φ)
A = amplitude, ω = angular frequency, φ = initial phase.
Time period: T = 2π/ω Frequency: f = 1/T = ω/2π
📈 Displacement-time graph for SHM
⚡ VELOCITY & ACCELERATION IN SHM
v = dx/dt = Aω cos(ωt + φ) = ± ω√(A² – x²)
a = d²x/dt² = –Aω² sin(ωt + φ) = –ω²x
Maximum velocity: vmax = Aω (at mean position)
Maximum acceleration: amax = Aω² (at extreme positions)
🔋 ENERGY IN SHM
Total mechanical energy is constant: E = (1/2)kA² = (1/2)mω²A²
KE = (1/2)mv² = (1/2)mω²(A² – x²)
PE = (1/2)kx² = (1/2)mω²x²
At extremes: KE=0, PEmax=E.
📊 Energy variation in SHM
🔧 SPRING-BLOCK OSCILLATOR
For a spring of constant k: ω = √(k/m), T = 2π√(m/k)
Series combination: 1/keff = 1/k₁ + 1/k₂
Parallel combination: keff = k₁ + k₂
🖍️ Spring-block system
⏱️ SIMPLE PENDULUM
For small oscillations (θ < 10°): T = 2π√(L/g)
ω = √(g/L), f = (1/2π)√(g/L)
Restoring force: F = –mg sinθ ≈ –mgθ (for small θ)
Effective g due to acceleration: T = 2π√(L/geff)
🧵 Simple pendulum
📉 DAMPED & FORCED OSCILLATIONS
Damped Oscillations
Amplitude decreases exponentially: A = A₀e–bt
Types: underdamped, critically damped, overdamped.
Forced Oscillations & Resonance
When driving frequency matches natural frequency, amplitude becomes maximum → resonance.
💡 NEET TIPS & SHORTCUTS
- In vertical spring, equilibrium position shifts but ω = √(k/m) remains same.
- For a spring of mass ms, effective mass = m + ms/3 in T formula.
- In compound pendulum, T = 2π√(I/mgd).
- For a body in SHM, average KE = average PE = E/2.
⚠️ COMMON MISTAKES
- Using ω = √(g/L) for spring instead of √(k/m).
- Forgetting to convert angle to radians in pendulum formulas.
- Assuming SHM is only sinusoidal – phase difference matters in superposition.
- Confusing angular frequency ω with angular velocity.
📌 QUICK REVISION CARD
SHM equation: x = A sin(ωt + φ)
ω = 2π/T = 2πf
vmax = Aω, amax = Aω²
Spring T: T = 2π√(m/k)
Pendulum T: T = 2π√(L/g)
Total energy: E = ½kA² = ½mω²A²