Simple Harmonic Motion (SHM)

Objective Questions – Page 5 (JEE Advanced Extreme Level)

SECTION: Rank-Deciding Conceptual Problems

A particle executes SHM. The ratio of maximum kinetic energy to maximum potential energy is:
Answer: 1
The displacement where speed is half of maximum speed is:
Answer: (√3/2)A
In SHM, the particle spends maximum time in which region?
Answer: Near extreme positions
If phase difference between two SHMs is π/2, the time difference is:
Answer: T/4
The instantaneous power delivered by restoring force is zero at:
Answer: Mean position
The average kinetic energy over one complete cycle is:
Answer: E/2
A particle crosses the mean position with speed v. At what displacement will its speed become v/2?
Answer: x = (√3/2)A
If angular frequency doubles, the time period becomes:
Answer: Half
Which of the following is independent of amplitude?
Answer: Time period
The phase angle when acceleration is half of maximum acceleration is:
Answer: π/6
If total energy is doubled, the amplitude becomes:
Answer: √2 times
The slope of velocity–displacement graph at mean position is:
Answer: −ω
In SHM, jerk (da/dt) is maximum at:
Answer: Mean position
The ratio of time taken to move from x = 0 to x = A/√2 and from x = A/√2 to x = A is:
Answer: Less than 1
Which method is safest for long SHM problems in JEE Advanced?
Answer: Energy method
If displacement is written as x = A cos(ωt + φ), the initial phase is:
Answer: φ
The acceleration at x = A/2 is:
Answer: −(ω²A)/2
The restoring force is proportional to:
Answer: Displacement
The time taken to go from +A to −A is:
Answer: T/2
Which quantity decides the nature of SHM?
Answer: Restoring force law

JEE ADVANCED WARNING:
Never compare displacements directly. Always convert displacement → phase angle → time.

Topper Trick:
If a question mentions:

Average value → integrate
Time ratio → phase difference
Energy → avoid equations of motion

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