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⚛️ Physics  ·  Oscillations  ·  NEET & JEE

The amplitude of a damped oscillator falls to one-third of its initial value in 10 s. After 20 s from the start its amplitude will be:

Answer: A 0 /9.

  • A A<sub>0</sub>/6
  • B A<sub>0</sub>/9
  • C A<sub>0</sub>/3
  • D A<sub>0</sub>/27

Correct answer: B. A<sub>0</sub>/9

Explanation: Amplitude decays as A = A<sub>0</sub>e<sup>-&gamma;t</sup>. At 10 s, e<sup>-10&gamma;</sup> = 1/3. At 20 s, e<sup>-20&gamma;</sup> = (1/3)<sup>2</sup> = 1/9, so the amplitude is A<sub>0</sub>/9.

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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