The following differential equations represent oscillating springs.

(i) $36 s'' + s = 0$, $s(0)= 12$, $s'(0) = 0$.
(ii) $s'' + 36 s = 0$, $s(0)= 2$, $s'(0) = 0$.
(iii) $9 s'' + s = 0$, $s(0)= 6$, $s'(0) = 0$.
(iv) $s'' + 9 s = 0$, $s(0)= 3$, $s'(0) = 0$.

Which differential equation represents:
(a) The spring oscillating most quickly (with the shortest period)? ? i ii iii iv
(b) The spring oscillating with the largest amplitude? ? i ii iii iv
(c) The spring oscillating most slowly (with the longest period)? ? i ii iii iv
(a) The spring oscillating with the largest maximum velocity? ? i ii iii iv