JEE Advanced – Simple Harmonic Motion (SHM)
Tough Numerical Problems with Full Solutions – Page 3
Level: Advanced | Multi-step | Time-pressure oriented
Q16. SHM with Sudden Stop
A particle of mass m performs SHM with amplitude A. At displacement x = A/2, the particle is suddenly stopped. Find the new amplitude of motion.
Solution:
Velocity at x = A/2:
v² = ω²(A² − x²) = ω²(A² − A²/4) = (3/4)ω²A²
New energy = kinetic energy at that point:
½mω²A'² = ½m v² = ½m(3/4)ω²A²
⇒ A'² = 3A² / 4
Answer: A' = (√3 / 2) A
Trap: Do NOT reuse original amplitude after stopping.
Q17. SHM with Changing Force Constant
Spring constant is suddenly doubled when particle is at mean position. Find ratio of new amplitude to old amplitude.
Solution:
At mean position, velocity is maximum.
Initial energy:
E = ½kA²
New spring constant = 2k
½(2k)A'² = ½kA² ⇒ A' = A / √2
Answer: A' : A = 1 : √2
Q18. SHM on Smooth Incline
A block attached to spring oscillates on a smooth incline. Does angle of incline affect time period?
Solution:
Gravity component shifts equilibrium position only.
Time period depends on m and k only.
Answer: Time period is independent of angle
JEE Insight: Forces changing equilibrium ≠ restoring forces
Q19. Maximum Jerk in SHM
Find position where jerk is maximum.
Solution:
Jerk = da/dt = −ω²v
|jerk| ∝ |v|
Velocity is maximum at mean position.
Answer: Mean position
Q20. Phase Difference & Energy Ratio
Two particles have same SHM but phase difference π/3. Find ratio of their potential energies when one is at mean position.
Solution:
At mean position, PE₁ = 0
For second particle:
x = A sin(π/3) = (√3/2)A
PE₂ = ½k x² = 3/4 (½kA²)
Answer: 0 : 3/4
Q21. SHM with Damping (Conceptual)
If damping force is introduced, which quantity remains constant?
- Amplitude ❌
- Energy ❌
- Frequency (approximately) ✅
- Phase ❌
Answer: Frequency (for light damping)
Q22. Velocity Distribution
At what fraction of amplitude does velocity become half of maximum?
Solution:
v = ω√(A² − x²) = vmax/2
⇒ A² − x² = A²/4 ⇒ x = (√3/2)A
Answer: x = (√3/2)A
Why Page 3 Is Rank-Deciding
- Combines sudden change + energy logic
- Tests understanding beyond formulas
- Matches hardest JEE Advanced numericals
- Builds calmness for lengthy questions
JEE Advanced SHM – Page 3 Completed ✅
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🔹 Simple Harmonic Motion (SHM) — Core Series
Coverage: Concepts → PYQs → Advanced Thinking → Exam Readiness
- SHM – Final Exam Day Checklist
- SHM Part 2
- SHM Part 3
- SHM Part 4
- SHM Part 5
- SHM Part 6
- SHM Part 7
- SHM Part 8
- SHM Part 9
- SHM Part 10
- SHM Part 11
- SHM Part 12
- SHM Part 13
- SHM Part 14
- SHM Part 15
- SHM Part 16
- SHM Part 17
- SHM Part 18
- SHM Part 19
- SHM Part 20
- SHM Part 21
- SHM Part 22
- SHM Part 23
- SHM Part 24
- SHM Part 25
- SHM Part 26
- SHM Part 27
- SHM Part 28
- SHM Part 29
🔹 Simple Harmonic Motion (SHM) — Extended Series (30–56)
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