Simple Harmonic Motion (SHM)

Objective Questions – Page 6 (JEE Advanced Level)

SECTION: Time, Phase & Graph-Based Questions

Time taken by a particle to move from x = A/2 to x = A/√2 is best found using:
Answer: Phase angle method
If displacement is zero at t = 0 and velocity is positive maximum, the equation is:
Answer: x = A sin(ωt)
A particle spends minimum time in which region?
Answer: Near mean position
The slope of acceleration–displacement graph is:
Answer: −ω²
At what displacement is kinetic energy equal to potential energy?
Answer: x = A/√2
The time taken to move between two points symmetric about mean position is:
Answer: Equal
If phase angle changes from π/6 to π/3, the time taken is:
Answer: T/12
The velocity is maximum when acceleration is:
Answer: Zero
The particle crosses x = A/2 twice in one cycle. The time difference is:
Answer: Less than T/2
The graph between kinetic energy and displacement is:
Answer: Parabolic
The average speed over one complete SHM is:
Answer: (2ωA)/π
In SHM, the particle has same speed at two different displacements because:
Answer: Energy conservation
Which quantity changes sign periodically?
Answer: Velocity
The time taken to go from x = A/√2 to x = −A/√2 is:
Answer: T/4
The displacement-time graph is sinusoidal because:
Answer: Restoring force is linear
The ratio of max acceleration to max velocity is:
Answer: ω
If ω increases, which quantity increases?
Answer: Maximum acceleration
Which remains constant throughout SHM?
Answer: Total mechanical energy
Time period depends on:
Answer: System parameters only
For large displacement questions, best approach is:
Answer: Energy + phase

JEE ADVANCED TRAP:
Never calculate time using velocity equation directly. Always convert x → θ → t.

Topper Strategy:
If question mentions:

“Time between two positions” → Phase angle
“Same speed” → Energy conservation
“Graph” → Slope meaning

Objective Page–6 Completed Successfully ✅

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