so for the last question, I balanced forces correctly and got acceleration = -392x, so w2=(392) - (think that's right), and then I got the suvat bit correct where you work out that the speed after they coalesce is 2.1ms-1, but after that, I tried to conserve energy and did so wrongly, getting an incorrect amplitude of 0.105-0.025= ~0.8, but then for the final step here's my working:
x=asin(wt), so x=asin(root(392)t)
but even though my value of a is wrong, surely the time at which the particle reaches its highest height is when x=a (it's at its amplitude and so x/a is just 1, meaning sin(wt)=1 and then wt= pi, 5(pi)/2, etc..., and the first case is when it's at the lowest point, so the highest point is (root(392))t = 5(pi)/2, and t= ~0.4, and adding on the 2/7 which is the initial time that Q falls for, I got T=0.682
However, as I right this I think maybe I should have considered x=-a too, meaning wt=3(pi)/2 would be the next solution, and so in hindsight I think the answer should have been 3(pi)/2 divided by root(392), = 0.238, + 2/7 = 0.524 ??
If that IS the answer, I'd imagine I would just lose 1 or 2 method marks, as well as the answer mark, and 4/7 is alright considering I did fine on questions 1, 2, 3, and 6.