It is well known that the solution for SHM with (
when
) is:
with
where
is the amplitude of oscillations and
.
Now in the first instance when the particle is at
let the time be
and let
so then
and
which after dividing gives us:
.
Similarly in the second instance when the particle is at
let the time be
and so then
and
which after dividing gives us:
. (Note this is in 2nd quadrant).
Thus (taking into account the quadrants) we have:
so
Hence
.