Solution to Differential Equation: Particle Motion with Initial Velocity of 2k

[squenshl]

Homework Statement

The equation of motion of a particle is given by the differential equation ##\frac{d^2x}{dt^2} = -kx##, where ##x## is the displacement of the particle from the origin at time ##t##, and ##k## is a positive constant.

1. Show that ##x = A\cos{(kt)}+B\sin{(kt)}##, where ##A## and ##B## are constants, is a solution of the equation of motion.
2. The particle was initially at the origin and moving with velocity ##2k##. Find the constants ##A## and ##B##.

Homework Equations

The Attempt at a Solution

I know for 1. just show LHS = RHS which I have done but a little lost on 2.
Please help!

 

[blue_leaf77]

The particle was initially at the origin and moving with velocity 2k2k2k.

That means ##x(0)=0## and ##x'(0) = 2k##. With these two equations, you are supposed to express ##A## and ##B## in terms of the known quantities.