A damped mass spring system with values of:

$c=100k\frac{g}{s}$

$m=100kg$

$k=1000\frac{N}{m}$

is subject to a force of $10cos(3t)$ in Newtons. The system is also subjected to initial conditions of:

$x_0=1mm,V_o=20m\frac{m}{s}.$

Calculate the following:

Mass Normalized force $($fo$)$ in $($N$/$kg$)$

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Natural Frequency $($rad$/$s$)$

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Damping Ratio

Damped Frequency

Amplitude of the particular solution $(x)$ in meters

Phase of the Particular solution $($Theta$)$ in radians.

Amplitude of the transient Solution $($A$)$ in meters.