Oscillations & Simple Harmonic Motion (SHM)
Phase 1 – Page 1 | IIT/JEE Solved Problems (Basic → Moderate)
Problem 1: Identifying SHM (Conceptual)
A particle moves along x-axis such that acceleration is given by a = −9x. Determine whether the motion is SHM and find its time period.
Solution:
Given:
a = −9x
Comparing with SHM equation:
a = −ω²x
⇒ ω² = 9 ⇒ ω = 3 rad/s
Time period:
T = 2π / ω = 2π / 3 s
IIT Thinking:
First identify SHM form → then extract ω.
Problem 2: Maximum Velocity in SHM
A particle executes SHM with amplitude 0.2 m and time period 2 s. Find its maximum velocity.
Solution:
ω = 2π / T = π rad/s
vmax = ωA = π × 0.2
vmax = 0.2π m/s
Problem 3: Displacement at Given Time
A particle executes SHM described by:
x = 0.1 sin(10t)
Find displacement at t = π/20 s.
Solution:
x = 0.1 sin(10 × π/20)
x = 0.1 sin(π/2) = 0.1 m
Problem 4: Energy Ratio in SHM
At what displacement does the kinetic energy become equal to potential energy?
Solution:
KE = PE
½mω²(A² − x²) = ½mω²x²
⇒ A² − x² = x²
⇒ x = A / √2
Answer: Displacement = A / √2
Problem 5: Time Period Change (Spring System)
The mass attached to a spring is increased four times. Find the new time period.
Solution:
T ∝ √m
If m → 4m:
T' = 2T
Problem 6: Simple Pendulum on Moon
If time period of a pendulum on Earth is 2 s, find its time period on Moon (gmoon = g/6).
Solution:
T ∝ 1 / √g
Tmoon = √6 × Tearth
Tmoon = 2√6 s
Problem 7: Velocity at Given Displacement
A particle executes SHM with amplitude A. Find velocity when displacement is x.
Solution:
v = ω√(A² − x²)
Velocity decreases as displacement increases.
Problem 8: Identifying Non-SHM
Which of the following motions is NOT SHM?
- A) Projection of uniform circular motion
- B) Simple pendulum (small angle)
- C) Particle moving with constant speed in circle
- D) Mass-spring system
Answer: C
IIT Trap:
Circular motion itself is NOT SHM — only its projection is.
Key Takeaways (Phase 1 – Page 1)
- Always identify SHM equation first
- Extract ω correctly
- Use energy relations smartly
- Avoid mixing f and ω
Phase 1 – Page 1 Completed Successfully ✅
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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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