SHM question (1 Viewer)

[YBK]

A particle is performing Simple Harmonic motion about a fixed point O in a straight line. At time t seconds it has displacement x meters from O given by x = cos2t - sin2t

i) Express x in the form R(cos2t+a) for some R>0 and 0<a<pie/2
ii) Find the amplitude and the period of the motion.
iii) determine whether the particle is initially moving towards O or away from O and whether it is initally speeding up or slowing down.
iv) Find the time at which the particle first returns to its starting point.



I can't do the first part of the question

any help would be great! thanks

 

[Riviet]

Start with:
cos2t - sin2t = Rcos(2t+a)
=Rcos2t.cosa - Rsin2t.sina
=Rcosa.cos2t - Rsina.sin2t

Then equate coefficients of cos2t and sin2t:
Rcosa = 1
Rsina = 1

Solve these two equations for R and a.