📚 IIT–JEE Physics Complete Learning Hub

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🔹 Core Physics Libraries

• 🔁 Simple Harmonic Motion (SHM) – Complete Library (IIT–JEE Advanced)
• 🌊 Mechanical Waves – JEE Advanced Objective Library
• 🧠 IIT–JEE Physics Complete Master Library

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• 🌐 Shaktimatha Learning Resource Hub
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📌 Structured • Exam-Oriented • IIT–JEE Advanced Focused Learning

Simple Harmonic Motion (SHM) – Tough Objective Questions

Stage-1 | Page-2 | JEE Advanced Level

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Q6. A particle performs SHM with amplitude A. The ratio of time taken to move from x = 0 to x = A/2 and from x = A/2 to x = A is:

Options:
A) 1 : 1 B) 1 : 2 C) 2 : 1 D) 1 : 3

Answer: C
Explanation:
Time ∝ phase change 0 → A/2 ⇒ θ = 0° → 30° A/2 → A ⇒ 30° → 90° Ratio = 30 : 60 = 1 : 2 ⇒ Inverse speed ⇒ 2 : 1

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Q7. The total energy of a particle executing SHM is E. At what displacement does the kinetic energy become 3E/4?

Options:
A) A/2 B) A/√2 C) A/√3 D) A/4

Answer: A
Explanation:
K = E − ½mω²x² = 3E/4 ⇒ x² = A²/4 ⇒ x = A/2

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Q8. In SHM, the magnitude of acceleration is maximum at:

Options:
A) Mean position B) Extreme position C) x = A/2 D) Everywhere same

Answer: B
Formula: a = ω²A (maximum)

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Q9. The phase difference between displacement and velocity in SHM is:

Options:
A) 0 B) π/2 C) π D) π/4

Answer: B
Concept: Velocity leads displacement by π/2.

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Q10. A particle in SHM crosses the mean position with speed v. What is its speed at displacement A/2?

Options:
A) v B) v/2 C) v√3/2 D) v/√2

Answer: C
Explanation:
v = ωA v_x = ω√(A² − x²) = ω√(A² − A²/4) = ωA√3/2

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