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)

Question

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)

Infinity Learn · Accepted Answer

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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