Simple Harmonic Motion (SHM)

Objective Questions – Page 9 (JEE Advanced Numerical Level)

SECTION: Numerical & Calculation-Based Traps

A particle executes SHM with amplitude 10 cm and time period 2 s. The maximum velocity is:
Answer: π m/s
If ω = 10 rad/s and A = 0.2 m, maximum acceleration is:
Answer: 20 m/s²
The ratio of maximum acceleration to maximum velocity is:
Answer: ω
If total energy is E, potential energy at x = A/2 is:
Answer: E/4
At what displacement is kinetic energy three times potential energy?
Answer: x = A/2
If amplitude is doubled, time period becomes:
Answer: Same
The time taken to go from mean position to x = A/2 is:
Answer: T/12
The average speed of a particle in SHM over one complete cycle is:
Answer: (2ωA)/π
If the phase angle changes by π/3, the time taken is:
Answer: T/6
For displacement x = A/√2, the velocity is:
Answer: v_max/√2
At extreme position, acceleration is:
Answer: ω²A
If angular frequency doubles, time period becomes:
Answer: Half
The maximum kinetic energy is proportional to:
Answer: A²
If x = A cos(ωt), velocity equation is:
Answer: −Aω sin(ωt)
Time spent by particle between x = 0 and x = A/2 is:
Answer: Less than T/4
The restoring force at x = A/2 is:
Answer: Half of maximum
Which quantity is independent of mass?
Answer: Time period (spring–mass SHM excluded)
The graph of total energy vs displacement is:
Answer: Straight line parallel to x-axis
The speed of particle is same at displacements +x and −x because:
Answer: Energy conservation
Which method is safest for long numerical problems?
Answer: Energy method

JEE ADVANCED TRAP:
Never substitute numbers first. Reduce the expression symbolically — then substitute.

Topper Shortcut:

Time → Phase angle
Speed at position → Energy
Graph → Slope meaning

Objective Page–9 Completed Successfully ✅

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