(Solved): Damped oscillators are complicated. For simplified cases, the amplitude of the damped oscillator de ...

Damped oscillators are complicated. For simplified cases, the amplitude of the damped oscillator decreases exponentially according to the equation $x=x_0{e}^{\frac{-bt}{2m}}$, where $x_0$ is the maximum amplitude at the start of the oscillation, $t$ is the time at which you calculate the amplitude, $m$ is the mass on the spring, and $b$ is a damping constant in $\mathrm{kg}/\mathrm{s}$. If $b=0.080\mathrm{kg}/\mathrm{s}$, $m=0.30\mathrm{kg}$, and the starting amplitude is $8.5\mathrm{cm}$, calculate the value for $x$ at the following times: a) $0.1\mathrm{s}$ b) $1.5\mathrm{s}$ c) $15.5\mathrm{s}$ d) $3.0\min$ e) $5.2\mathrm{h}$