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

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

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