$3.$ i$)$ A $4\mathrm{.}00$ kg block hangs from a spring, extending it by $16\mathrm{.}0$ cm from its unstretched position. $($a$)$ Calculate the spring constant. $($b$)$ The block is removed, and a $0\mathrm{.}200$ kg body is hung from the same spring. Calculate the period of oscillation of the spring with this body attached, if the spring is stretched and then released. $(10$ marks$)$ ii$)$ Starting from rest at t $=0,$ a wheel undergoes a constant angular acceleration. When t $=2\mathrm{.}0$ s$,$ the angular velocity of the wheel is $5\mathrm{.}0$ rad$/$s$.$ The acceleration continues until t $=20\mathrm{.}0$ s$,$ when it abruptly ceases. Through what angle does the wheel rotate in the interval t $=0$ to $40$ s$?(15$ marks$)$