Stage–3 | Page–1
Energy in Simple Harmonic Motion (IIT–JEE Advanced)

This stage converts formulas into instant visualization


Core Idea of Energy in SHM

In SHM, energy is not destroyed or created — it only transforms between kinetic and potential forms.

Total Mechanical Energy = Constant

Types of Energy in SHM

  • Kinetic Energy (K)
  • Potential Energy (U)
  • Total Energy (E)

Potential Energy in SHM

U = ½ kx²
  • Minimum at mean position
  • Maximum at extreme positions
  • Always positive

Graph: Parabola opening upward


IIT Trap #1 – Zero Potential Confusion

  • U = 0 only at mean position
  • Extreme position ≠ zero energy

Kinetic Energy in SHM

K = ½ mω²(A² − x²)
  • Maximum at mean position
  • Zero at extreme positions

Graph: Inverted parabola


Total Energy of SHM

E = ½ kA² = constant
  • Independent of time
  • Independent of position

Energy Transformation During Motion

Position Kinetic Energy Potential Energy
Mean Position Maximum Zero
Extreme Position Zero Maximum
Intermediate Partial Partial

Fraction of Energy (Advanced Focus)

At displacement x:

K / E = 1 − (x² / A²)
U / E = x² / A²

IIT Trap #2 – Half Energy Myth

  • K = U does NOT occur at x = A/2
  • Occurs at x = A / √2

Finding Speed Using Energy

v = ω√(A² − x²)
  • Fastest method in JEE
  • Avoid time equations when possible

Typical JEE Advanced Questions

  • Find position where K = nU
  • Compare energies at two positions
  • Energy ratios without time
  • Graph matching questions

Topper Insight

If energy is involved, forget time. Energy problems are geometry, not algebra.

Next Pages in Stage–3

  • Page–2: Energy vs Time Graphs
  • Page–3: Turning Points & Energy Barriers
  • Page–4: Advanced PYQs on Energy

Stage–3 | Page–1 Completed ✔ Energy foundation is now unshakeable ⚡

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