Question

A spring oscillator is designed with a mass of 0.110 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 9.12 s. Find the required damping constant for the system. Please Answer in kg/s

Answer 1

Answer on Question #54953-Physics-Mechanics-Kinematics-Dynamics

A spring oscillator is designed with a mass of $0.110\,\mathrm{kg}$. It operates while immersed in a damping fluid, selected so that the oscillation amplitude will decrease to $1.00\%$ of its initial value in 9.12 s. Find the required damping constant for the system. Please Answer in kg/s

Solution

The equation for amplitude is

$$A = 0.01 A_{\max} = A_{\max}$$ $$e^{-\frac{b}{2m} T} = 0.01$$ $$\frac{b}{2m} = -\frac{\ln 0.01}{T} = -\frac{\ln 0.01}{9.12\,\mathrm{s}} = 0.505\,\mathrm{s}^{-1}.$$

Damping constant is

$$b = 0.505\,\mathrm{s}^{-1} \cdot 2 \cdot 0.110\,\mathrm{kg} = 0.111\,\frac{\mathrm{kg}}{\mathrm{s}}.$$

Answer: $0.111\,\frac{\mathrm{kg}}{\mathrm{s}}$.

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