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Q.

A 21.2kg object oscillates at the end of a vertical spring that has a spring constant 20500 Nm–1. The effect of air resistance is represented by the damping coefficient b = 2 Nsm–1. Find the time interval that elapses while the energy of the system drops to 10% of its initial value (Given, ln 10 = 2.302)

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a

34.4s

b

12.2s

c

24.4s

d

8.9s

answer is C.

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Detailed Solution

τ=mb=21.22=10.6sE=E0e−t/τ⇒0.1=e−t/10.6et/10.6=10⇒t10.6=ln⁡10t=(10.6)(2.302)=24.4s

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A 21.2kg object oscillates at the end of a vertical spring that has a spring constant 20500 Nm–1. The effect of air resistance is represented by the damping coefficient b = 2 Nsm–1. Find the time interval that elapses while the energy of the system drops to 10% of its initial value (Given, ln 10 = 2.302)