ok, ive got the book and im looking at Q6 Ai from 1998...
firstly its not a simple harminc motion (SHM) question.
SHM is characterised but a point oscillating round a point... that is for instant a clock pedulum moving back and forth.
this is a projectile question
you were on the right track though with you initial velocties... this is a process that you should just learn off, because you often cant do any of the question without the formulas that the process derive.
so ultimatly the question is asking you for the function that the projectile makes. to find that you first have to find x in terms of t, and y in terms of t. to do this you have to start with the initial velocites which are:
x'=VcosO
y'=VsinO
and sustitue 45 in for the angle
that is what the answer is substituting in for C1.
they havent been overly clear in the answer, but they are finding their horizontal and vertical motions in the answer... so jsut go to your notes and follow that process...
integrating
x''=0 and y''=-g
then you can make a cartesian out of you x and y formula thingy's
goodluck
