For a certain damped oscillator the damping constant is and the initial mechanical…

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

For a certain damped oscillator the damping constant is

\beta = 0.080\,\text{s}^{-1}

and the initial mechanical energy stored in the system is

18\,\text{J}

. (i) Derive an expression connecting the mechanical energy

E

at time

t

with

\beta

and the initial energy

E_0

. (ii) Using your result, find the time required for the energy to drop to

2.0\,\text{J}