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Oscillations – Complete Formula & Question Profiling

Oscillations – Complete Formula & Question Profiling (JEE Main Only)

1. Periodic & Oscillatory Motion

  • Periodic motion: Repeats itself after equal intervals of time
  • Oscillatory motion: To-and-fro about mean position
  • All oscillatory motions are periodic (not vice-versa)

2. Simple Harmonic Motion (SHM)

Defining condition:

a ∝ −x

a = −ω²x

  • Restoring force always towards mean position

3. SHM Kinematics

Displacement:

x = A sin(ωt + φ)

Velocity:

v = ω√(A² − x²)

Acceleration:

a = −ω²x

Maximum values:

  • vmax = ωA
  • amax = ω²A

4. Time Period & Frequency

T = 2π / ω
f = 1 / T

  • Independent of amplitude (for SHM)

5. Mass–Spring System

ω = √(k / m)

T = 2π√(m / k)

  • Horizontal and vertical springs → same T
  • Extension due to gravity does not affect T

6. Simple Pendulum

T = 2π√(l / g)

  • Valid for small angular displacement
  • Independent of mass

Effective length change:

  • In lift accelerating upward → g' = g + a
  • In lift accelerating downward → g' = g − a

7. Energy in SHM

Kinetic Energy:

K = ½ mω²(A² − x²)

Potential Energy:

U = ½ mω²x²

Total Energy:

E = ½ mω²A² = constant

  • At mean position → KE max
  • At extreme → PE max

8. Phase & Phase Difference

Phase: ωt + φ

  • Same phase → zero phase difference
  • Opposite phase → π rad

9. Damped Oscillations

  • Amplitude decreases with time
  • Energy continuously lost
  • Time period slightly increases

10. Forced Oscillations & Resonance

  • External periodic force applied
  • Resonance → max amplitude when driving freq = natural freq
  • At resonance → energy absorption maximum

11. JEE Main Question Profiling

Question Type JEE Tests Common Trap
SHM definition a ∝ −x condition Ignoring negative sign
Energy based MCQ KE–PE exchange Wrong position substitution
Spring–block k/m dependence Gravity affecting T
Pendulum in lift Effective g concept Sign error in g'
Resonance Frequency matching Confusing amplitude & energy
Phase questions Trigonometric understanding Using degrees instead of radians

12. JEE Main Weightage Insight

  • 1–2 MCQs in most sessions
  • Formula-heavy, concept-light
  • Very high scoring chapter

StudyBeacon • JEE Main Physics • Oscillation Master Sheet

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