Dynamic system response

Given: A spring$-$mass$-$damper system is set up with the following properties: mass $\backslash ($ m$=22\mathrm{.}8\backslash$mathrm$\{$~g$\}\backslash ),$ spring constant $\backslash ($ k$=51\mathrm{.}6\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$cm$\}\backslash ),$ and damping coefficient $\backslash ($ c$=3\mathrm{.}49\backslash$mathrm$\{$~N$\}\backslash$cdot $\backslash$mathrm$\{$~s$\}/\backslash$mathrm$\{$m$\}\backslash )(\backslash ($ c $\backslash )$ is also called $\backslash (\backslash$lambda $\backslash )$ in some textbooks$).$ The forcing function is a step function $($sudden jump$).$

$($a$)$ Calculate the damping ratio of this system. Will it oscillate?

$($b$)$ If the system will oscillate, calculate the oscillation frequency in hertz. $[$Note: Calculate the physical frequency, not the radian frequency.$]$ Compare the actual oscillating frequency to the undamped natural frequency of the system.