A 2.77-kg mass attached to a spring with k = 145 N/m is oscillating in a vat of

Question

A 2.77-kg mass attached to a spring with k = 145 N/m is oscillating in a vat of oil, which damps the oscillations.

a) If the damping constant of the oil is b = 11.3 kg/s, how long will it take the amplitude of the oscillations to decrease to 1.70 % of its original value?


b) What should the damping constant be to reduce the amplitude of the oscillations by 98.3 % in 1.80 s?

Explanation / Answer

b^2-4mk < 0 --> we have under dumped system --> amplitude will behave like a exp(-bt/2m) need to find at what t exp will be 0.017 --> exp(-bt/2m)=0.017 --> bt/2m=4.07 --> t= 2 sec b) exp(-bt/2m)=0.017, t=1.8 sec --> bt/2m=4.07 --> b=12.52

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