JEE Advanced – Simple Harmonic Motion (SHM)
Previous-Year Level Questions with Solved Answers
Concept → Method → Calculation → Insight
Q1. Energy Equality in SHM
A particle performs SHM with amplitude A. At what displacement will its kinetic energy equal potential energy?
Solution:
Total Energy:
E = ½ kA²
At displacement x:
PE = ½ kx²
KE = ½ k(A² − x²)
Equating KE = PE:
½kx² = ½k(A² − x²)
2x² = A²
x = A / √2
Answer: ± A / √2
JEE Insight: Energy questions avoid time and phase completely.
Q2. Time from Mean to A/2
Time taken by a particle in SHM to move from x = 0 to x = A/2?
Solution:
x = A sin(ωt)
sin(ωt) = 1/2 ⇒ ωt = π/6
t = π / (6ω)
Since T = 2π / ω:
t = T / 12
Answer: T / 12
JEE Trick: Always convert time answers into fractions of T.
Q3. Maximum Acceleration
In SHM, at what position is acceleration maximum?
Solution:
a = −ω²x
|a| is maximum when |x| is maximum → x = ±A
Answer: At extreme positions
Examiner Trap: Many students wrongly answer “mean position”.
Q4. Effect of Doubling Amplitude
If amplitude of SHM is doubled, what happens to maximum speed?
Solution:
vmax = ωA
If A → 2A ⇒ vmax → 2vmax
Answer: Maximum speed doubles
Q5. Frequency & Acceleration Relation
Two SHMs have same amplitude but frequencies f₁ and f₂. Find ratio of maximum accelerations.
Solution:
amax = ω²A = (2πf)²A
a₁ / a₂ = (f₁ / f₂)²
Answer: (f₁ / f₂)²
Q6. Parallel Spring SHM
A mass m is attached to two identical springs (k) in parallel. Find time period.
Solution:
keq = k + k = 2k
T = 2π √(m / 2k)
Answer: 2π√(m / 2k)
Q7. Phase Difference for Cancellation
At what phase difference do two SHMs cancel completely?
Answer: 180° (π radians)
Q8. Velocity at Mean Position
Is velocity always maximum at mean position?
- Yes – in ideal SHM
- No – if damping or external forces exist
Examiner Thinking: Check if student assumes ideal conditions.
How JEE Toppers Approach SHM
- Decide energy / time / phase first
- Avoid blind formula writing
- Convert answers into T, A, ω form
- Use symmetry in motion
- Never mix linear & angular terms
JEE Advanced SHM – Solved PYQ Module Completed ✅
📚 IIT–JEE Physics Complete Library
Concept Mastery • PYQs • Strategy • Revision
One-stop structured learning hub
🔹 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)
These pages are placed separately for continuity & reference.
30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56
🔹 Supporting & Mega Libraries
✔ Library logically bifurcated • ✔ All links preserved • ✔ Student-first design
No comments:
Post a Comment