Question $)=(25$ : Consider the following spring$-$mass$-$damper system with $m=100kg,c=$

$100k\frac{g}{s},k=910\frac{N}{m}$ and is subjected to a harmonic force of $10cos(3t)N.$ The system is also

subject to initial condition of $x_0=0\mathrm{.}001m$ and $v_0=0\mathrm{.}02\frac{m}{s}.$

$($a$)$ Compute the amplitude and phase of the transient response if the amplitude and phase of

the steady$-$state responses are $0\mathrm{.}033$ m and $1\mathrm{.}537$ rad $,$ respectively.

$($b$)$ Write the expression of the total response, $x(t),$ i$.$e$.,$ transient response and steady$-$state

response together.