Question $2.$

$(30$ marks$)$

Figure $2$ shows the suspension of one front wheel of a car in which $L_1=0\mathrm{.}4$ m and $L_2=0\mathrm{.}6m.$ The coil spring has a spring constant of $k=3\mathrm{.}610\frac{N}{m}$ and the car weight associated with that wheel is $3500$ N $.$ Determine the suspension's natural frequency for vertical motion.

Figure $2$: Vehicle Suspension