JEE Advanced – Simple Harmonic Motion (SHM)
Ultra-Tough Problems (Top Rank Level) – Page 6
Warning: These questions test thinking, not memory.
Q31. SHM with Sudden Removal of Constraint
A block of mass m is executing SHM on a smooth surface attached to a spring. At the mean position, the spring is suddenly cut. Find the subsequent motion.
Solution:
- At mean position, velocity is maximum
- Once spring is cut → no restoring force
The block moves with uniform velocity equal to maximum speed.
Answer: Uniform motion with constant velocity
Examiner Trap: Many answer “particle stops” ❌
Q32. SHM with Instantaneous Change of Mass
A particle in SHM suddenly sticks to another identical particle at mean position. Find new time period.
Solution:
- Mass doubles → m → 2m
- Spring constant unchanged
T' = 2π√(2m / k) = √2 T
Answer: T' = √2 T
Q33. SHM + Projectile Coupling
A particle in SHM is released from mean position with velocity perpendicular to SHM line. Describe motion.
Solution:
- SHM along one axis
- Uniform motion along perpendicular axis
Answer: Resultant motion is sinusoidal path
Insight: Orthogonal motions are independent
Q34. Sudden Change in Phase
A particle performing SHM has its velocity reversed instantly at some position x. What happens to motion?
Solution:
- Magnitude of velocity same
- Direction reversed → phase changes
Amplitude remains same, phase changes by π
Answer: Same SHM, phase inverted
Q35. Maximum Power Condition
At what displacement is power maximum in SHM?
Solution:
Power = F·v = (−kx)(ω√(A² − x²))
Maximize |x√(A² − x²)|
x = A / √2
Answer: x = A / √2
Q36. SHM with Time-Dependent Amplitude
If amplitude decreases slowly due to damping, which quantity remains nearly constant?
- A. Energy
- B. Amplitude
- C. Frequency
- D. Phase
Answer: C (Frequency)
Q37. SHM Inside Lift
A spring-mass system oscillates inside a lift moving upward with acceleration a. Find effect on time period.
Solution:
Pseudo force shifts equilibrium only.
Answer: Time period unchanged
Why Page 6 is Rank-Deciding
- Tests sudden-change logic
- Combines multiple concepts
- Matches hardest JEE Advanced questions
- Separates top 1% from rest
JEE Advanced SHM – Page 6 (Ultra-Tough) 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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