JEE Advanced – Simple Harmonic Motion (SHM)

Previous-Year Level Problems (Advanced) – Page 2

Focus: Concept coupling, logical elimination, and examiner traps

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Q9. SHM with Suddenly Changed Amplitude

A particle performing SHM passes through mean position with speed v. Suddenly its amplitude becomes half. Find new maximum speed.

Solution:

At mean position, velocity depends only on total energy.

Original energy:
E = ½ m v²

New amplitude does not change instantaneous velocity.

Answer: New maximum speed = v

Trap: Amplitude change ≠ velocity change at mean position

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Q10. Particle Released from Extreme

A particle starts SHM from extreme position. Find ratio of time taken to go from x = A → A/2 and A/2 → 0.

Solution:

Use x = A cos(ωt)

For x = A/2:
cos(ωt₁) = 1/2 ⇒ ωt₁ = π/3

Time from A → 0: ωt₂ = π/2

Time A→A/2 : A/2→0 = (π/3) : (π/2 − π/3) = 2 : 1

Answer: 2 : 1

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Q11. Energy vs Displacement Graph

In SHM, which quantity varies linearly with x²?

• Kinetic Energy ❌
• Potential Energy ✅
• Velocity ❌
• Acceleration ❌

Because PE = ½kx²

Answer: Potential Energy

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Q12. SHM Under Gravity (Vertical Spring)

Does gravity affect time period of vertical spring SHM?

Solution:

Gravity only shifts mean position.

Time period depends on k and m only.

Answer: Time period is unchanged

JEE Insight: Forces affecting equilibrium ≠ forces affecting oscillation

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Q13. Phase Difference & Velocity

Two particles in SHM have phase difference π/2. If one is at mean position, where is the other?

Solution:

Phase difference π/2 ⇒ one sine, one cosine.

If first at x = 0 ⇒ second at x = ±A

Answer: At extreme position

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Q14. Maximum Power in SHM

At what position is power maximum in SHM?

Solution:

Power = F · v

• At mean position: F = 0
• At extreme position: v = 0

Maximum power occurs at intermediate position.

Answer: Between mean and extreme

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Q15. Angular SHM (Small Oscillations)

A disc oscillates with small angular displacement θ. Equation is:

I d²θ/dt² = −kθ

Identify motion.

Answer: Angular SHM

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How This Page Helps Rank Improvement

• Separates conceptual students from formula learners
• Tests assumption clarity
• Builds confidence for multi-step problems
• Directly matches JEE Advanced difficulty

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JEE Advanced SHM – Page 2 Completed ✅