For a damped simple harmonic oscillator, the block has a mass of $1\mathrm{.}8$ kg and the spring constant is $8\mathrm{.}2\frac{N}{m}.$ The damping force is given by $-b(d\frac{x}{d}t),$ where $b=230\frac{g}{s}.$ The block is pulled down $11\mathrm{.}9$ cm and released. $($a$)$ Calculate the time required for the amplitude of the resulting oscillations to fall to $\frac{1}{7}$ of its initial value. $($b$)$ How many oscillations are made by the block in this time?

$($a$)$ Number

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$($b$)$ Number

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