Stage–3 | Page–2
Energy Graphs in Simple Harmonic Motion

Graphs are the fastest weapons in JEE Advanced


Why Energy Graphs are Crucial

  • Most JEE Advanced questions are visual
  • Graphs avoid long calculations
  • Help instantly identify traps

1. Energy vs Displacement (x)

Potential Energy:

U = ½ kx²
  • Parabolic curve opening upward
  • Minimum at x = 0
  • Maximum at x = ±A

Kinetic Energy:

K = ½ mω²(A² − x²)
  • Inverted parabola
  • Maximum at x = 0
  • Zero at x = ±A

Total Energy:

E = constant (horizontal straight line)

Important Intersection Point

  • K = U when x = ± A / √2
  • Both equal to E / 2
⚠ IIT Favorite Point

2. Energy vs Time (t)

Assume displacement:

x = A sin(ωt)

Potential Energy vs Time:

U = ½ kA² sin²(ωt)
  • Always positive
  • Period = T/2

Kinetic Energy vs Time:

K = ½ kA² cos²(ωt)
  • Maximum when U is minimum
  • Period = T/2

IIT Trap – Period Confusion

  • Displacement period = T
  • Energy period = T/2
Energy repeats twice in one oscillation

Phase Relationship

Quantity Phase Relation
Displacement & Velocity 90°
Kinetic & Potential Energy 90°
Energy & Displacement Dependent on square

Area Under Energy–Time Graph

  • Represents energy × time
  • No physical work meaning
  • Used only for comparison

JEE Advanced Question Patterns

  • Identify correct graph
  • Compare energy at two times
  • Energy ratio from graph
  • Phase-based reasoning

Topper Strategy

Never calculate energy graph values point-by-point. Recognize shape → answer instantly.

Next in Stage–3

  • Page–3: Turning Points & Energy Barriers
  • Page–4: PYQs on Energy Graphs

Stage–3 | Page–2 Completed ✔ Graph mastery unlocked 📈

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