Oscillations & Simple Harmonic Motion
IIT / JEE Tough Objective Paper – 3
Q1. SHM with Energy Constraint
A particle executes SHM. At what displacement is the ratio of kinetic energy to potential energy equal to 1 : 3 ?
Solution:
KE : PE = 1 : 3 ⇒ KE = (1/4)E, PE = (3/4)E
PE / E = x² / A² ⇒ x² / A² = 3/4 ⇒ x = (√3/2)A
Answer: x = (√3/2)A
Q2. Time Calculation Trap
Time taken by a particle to move from displacement A/2 to mean position is:
Answer: T/12
JEE Trick:
Use phase method, not equations.
x = A cosθ → A/2 ⇒ θ = π/3
Mean ⇒ θ = π/2
Δθ = π/6 ⇒ Δt = (T/2π)(π/6) = T/12
Q3. Non-SHM Identification
Which of the following motions is NOT SHM?
- A) Small oscillations of pendulum
- B) Block on spring
- C) Circular motion projected on diameter
- D) Large angle pendulum motion
Correct Answer: D
Reason: Restoring force not proportional to displacement at large angles.
Q4. Acceleration Direction Trap
At a point between mean and extreme position, acceleration is:
- A) Zero
- B) Towards mean
- C) Away from mean
- D) Random
Correct Answer: B
IIT Rule: Acceleration always points toward mean position.
Q5. Combined Motion
A particle performs SHM along x-axis and uniform motion along y-axis. The resultant path is:
- A) Circle
- B) Ellipse
- C) Straight line
- D) Cycloid
Correct Answer: B
Q6. Maximum Velocity Location
Velocity is maximum when:
- A) x = A
- B) x = A/2
- C) x = 0
- D) x = −A
Correct Answer: C
Q7. Dimensional Analysis (Advanced)
Which expression gives time period dimensionally?
- A) √(k/m)
- B) √(m/k)
- C) m/k
- D) k/m
Correct Answer: B
Q8. Energy Graph Concept
Which graph is linear?
- A) KE vs x
- B) PE vs x
- C) a vs x
- D) v vs x
Correct Answer: C
Because a = −ω²x
Q9. Frequency Change
If spring constant becomes 4k, frequency becomes:
Answer: 2 times
Since f ∝ √k
Q10. Ultimate IIT Trap
A particle passes through mean position with speed v. What is speed at displacement A/2?
Solution:
v_max = ωA v = ω√(A² − (A/2)²) = ωA√(3/4) = (√3/2)v_max
Answer: (√3/2)v
IIT LEVEL TAKEAWAY:
• Phase method saves time
• Energy ratio → square relation
• Acceleration always toward mean
• Large angles break SHM
IIT Tough Objective Paper – 3 Completed ✅
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🔹 Simple Harmonic Motion (SHM) — Core Series
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- SHM – Final Exam Day Checklist
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🔹 Simple Harmonic Motion (SHM) — Extended Series (30–56)
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