Simple Harmonic Motion (SHM) – One Page Mind Map

IIT JEE • Intermediate • Quick Revision

1. Basic Condition of SHM

  • Restoring force ∝ displacement
  • Direction of force is always opposite to displacement
  • Mathematically: F = −kx

2. Displacement Equation

  • x = A sin(ωt + φ)
  • x = A cos(ωt + φ)

3. Velocity

  • v = dx/dt
  • v = Aω cos(ωt + φ)
  • vmax = Aω (at mean position)

4. Acceleration

  • a = dv/dt
  • a = −ω²x
  • amax = ω²A (at extreme position)

5. Energy in SHM

  • Kinetic Energy: KE = ½mv²
  • Potential Energy: PE = ½mω²x²
  • Total Energy = ½mω²A² (constant)

6. Time & Phase Concept

  • Phase: θ = ωt + φ
  • Time difference: Δt = Δθ / ω
  • Use phase method for all time-based questions

7. Important Graphs

  • x–t → sine curve
  • v–t → cosine curve
  • a–x → straight line (slope = −ω²)
  • KE–x → parabola

8. Exam Focus Areas

  • Mean position vs extreme position
  • Energy vs time
  • Symmetry between +x and −x

9. Traps & Shortcuts

  • Velocity is zero at extreme, not acceleration
  • Acceleration is zero at mean, not velocity
  • Energy is constant but KE & PE vary
  • Phase method saves time in JEE

Perfect SHM Revision Sheet for IIT JEE ✅

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🔹 Simple Harmonic Motion (SHM) — Core Series

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🔹 Simple Harmonic Motion (SHM) — Extended Series (30–56)

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