Decay Time of Damped Oscillator

Classical Mechanics Level 2

A 10 kg 10 \text{ kg} mass is attached to a spring of spring constant 10 N / m 10 \text{ N}/\text{m} . The entire system is submerged in water, which exerts a viscous damping force on the mass F d = − ( 2 N ⋅ s / m ) v F_d = -(2 \text{ N}\cdot \text{s}/\text{m}) \:v . The mass is pulled so that the spring is displaced from equilibrium by . 1 m .1 \text{ m} and is released. Find the 1 / e 1/e decay time of oscillation in seconds.


The answer is 10.

Matt DeCross by Matt DeCross , 27, USA

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1 solution

Matt DeCross
Feb 22, 2016

The 1 / e 1/e decay time for damped harmonic oscillators is τ = 2 m b \tau = \frac{2m}{b} . Plugging in,

τ = 20 kg 10 N ⋅ s / m = 10 s . \tau = \frac{20 \text{ kg}}{10 \text{ N}\cdot\text{s}/\text{m}} = 10 \text{ s}.

0 Helpful 1 Interesting 0 Brilliant 0 Confused

The mass and spring constant are extra information that is not required.

Indraneel Mukhopadhyaya - 4 years, 9 months ago

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I agree there is (deliberately) extra information here, but you should be able to see above that the mass is in fact required.

Matt DeCross - 4 years, 8 months ago

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Yes, mass is required.You are correct there.

Indraneel Mukhopadhyaya - 4 years, 8 months ago

how is b equal to 10?

Richa Sharma - 1 year, 10 months ago

Wouldn't b = 2, which then makes the decay time = 10? The solution states that 20/10 = 10. Seems like a typo.

David Paek - 1 year, 9 months ago

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