Question $6(20\backslash \%)$

$($a$)$ A mass of weight $90$ N is attached to the end of a spring. If the mass is released very slowly, the spring is extended with $100$ mm and reached static equilibrium. What is the natural frequency of the system in hertz?

$($b$)$ If the same mass is given an initial velocity of $\backslash (1\mathrm{.}6\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ downward from the position $50$ mm below the equilibrium position, what is the equation of displacement of the mass as a function of time

$($c$)$ Use the results from $($b$),$ draw a diagram to illustrate the displacement versus time behaviour and $/$ndicate important parameters of the vibration such as phase, amplitude, initial displacement, initial velocity, and period on the diagram.