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⚛️ Physics  ·  Oscillations  ·  NEET & JEE

The equation x = A e<sup>-bt/2m</sup> sin(ω_d t + φ) describes:

Answer: Underdamped oscillation.

  • A Underdamped oscillation
  • B Overdamped oscillation
  • C Critical damping
  • D Forced oscillation

Correct answer: A. Underdamped oscillation

Explanation: Underdamped oscillation: the system still oscillates but with exponentially decreasing amplitude. ω_d = √(ω_0² - b²/4m²) is the damped frequency.

Displacement, Velocity, Acceleration in SHMx(t)v(t)a(t)v leads x by 90°; a is exactly out of phase with x (a = −ω²x)

In SHM, displacement and velocity are 90° out of phase (v is maximum when x=0, and zero when x is extreme), while acceleration is always exactly opposite in sign to displacement, consistent with a = −ω²x.

Concept context

Simple harmonic motion, spring-mass, pendulum, energy in SHM, and resonance.

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