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.