A spring oscillator is designed with a mass of 0.205 kg. It operates while immer

Question

A spring oscillator is designed with a mass of 0.205 kg. It operates while immersed in a damping fluid, selected so that the oscillation amplitude will decrease to 1.00% of its initial value in 6.30 s. Find the required damping constant for the system.
Answer: ________ kg/s A spring oscillator is designed with a mass of 0.205 kg. It operates while immersed in a damping fluid, selected so that the oscillation amplitude will decrease to 1.00% of its initial value in 6.30 s. Find the required damping constant for the system.
Answer: ________ kg/s
Answer: ________ kg/s

Explanation / Answer

xmax(t) = Ae^(-bt/2m) equation 1

where A is amplitude, b is damping constant, m is mass

xmax(6.30)=.99A equation 2

and m= 0.205 kg

from equation 1 & 2

0.99 = e^(-b*6.3/2*.205)

b = -ln(0.99) *2*0.205/6.3

b = 6.54 * 10-4 kg/s

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