# Differential equation

1. Aug 24, 2016

### squenshl

1. The problem statement, all variables and given/known data
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 $B$.

2. Relevant equations

3. The attempt at a solution
I know for 1. just show LHS = RHS which I have done but a little lost on 2.
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.