Oscillations & Simple Harmonic Motion
Phase 1 – Page 4 | JEE Main–Style Numerical Problems
Problem 26: Time Period from Graph
The displacement of a particle executing SHM is given by x = 4 sin(10t). Find the time period.
Solution:
Comparing with x = A sin(ωt):
ω = 10 rad/s
Time period:
T = 2π / ω = 2π / 10 = π / 5 s
Problem 27: Maximum Speed
A particle executes SHM with amplitude 5 cm and time period 2 s. Find its maximum speed.
Solution:
Angular frequency:
ω = 2π / T = π rad/s
Maximum speed:
vmax = ωA = π × 0.05 = 0.157 m/s
Problem 28: Speed at Given Displacement
A particle executes SHM with amplitude 0.1 m and ω = 10 rad/s. Find its speed at displacement 0.06 m.
Solution:
Speed formula:
v = ω √(A² − x²)
Substitute values:
v = 10 √(0.01 − 0.0036) = 10 √0.0064 = 0.8 m/s
Problem 29: Acceleration at Given Position
Find the acceleration of a particle in SHM at displacement x = 0.04 m, if ω = 5 rad/s.
Solution:
Acceleration formula:
a = −ω²x
Substitute:
a = −25 × 0.04 = −1 m/s²
Problem 30: Mean Position Crossing Speed
A particle crosses the mean position with speed 2 m/s. What is its maximum speed?
Solution:
In SHM, speed is maximum at mean position.
vmax = 2 m/s
Problem 31: Energy Ratio
At what displacement does the kinetic energy become equal to potential energy?
Solution:
KE = PE when:
A² − x² = x²
⇒ x = A / √2
Answer: x = A / √2
Problem 32: Time for Half Oscillation
How much time does a particle take to go from one extreme to the other?
Solution:
One complete oscillation time = T
Time = T / 2
Problem 33: Phase Difference
Find the phase difference between displacement and velocity in SHM.
Solution:
Velocity leads displacement by:
π / 2 radians
Problem 34: Direction of Acceleration
What is the direction of acceleration when the particle is at positive displacement?
Solution:
Acceleration always points toward mean position.
Direction: Negative
JEE Main Strategy Notes (Phase 1 – Page 4)
- Graph-based equations give ω directly
- Use v = ω√(A² − x²) to save time
- Acceleration sign matters in conceptual MCQs
- Mean position facts are frequently tested
Phase 1 – Page 4 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
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- 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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