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A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations.  The time it will take to drop to  of the original amplitude is close to

(a)

100 s

(b)

10 s

(c)

50 s

(d)

20 s



Question ID - 51177 | SaraNextGen Top Answer

A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations.  The time it will take to drop to  of the original amplitude is close to

(a)

100 s

(b)

10 s

(c)

50 s

(d)

20 s

1 Answer
127 votes
Answer Key / Explanation : (d) -

Time for 10 oscillations =  = 2 s

A = A0 e – kt

   = e −2k                    ⇒ ln2 = 2k

10 −3 = e −kt               ⇒ 3ln10 = kt

t =  × 2

  = 6 ×    20 s

127 votes


127