Solving the differential equation above produces a solution that is a sinusoidal function : x ( t ) = c 1 cos ⁡ ⁡ ( ω ω t ) + c 2 sin ⁡ ⁡ ( ω ω t ) , where ω ω = k / m . The meaning of the constants c 1 and c 2 can be easily found: setting t = 0 on the equation above we see that x ( 0 ) = c 1 , so that c 1 is the initial position of the particle, c 1 = x 0 ; taking the derivative of that equation and evaluating at zero we get that x ˙ ˙ ( 0 ) = ω ω c 2 , so that c 2 is the initial speed of the particle divided by the angular frequency, c 2 = v 0 ω ω . Thus we can write: x ( t ) = x 0 cos ⁡ ⁡ ( k m t ) + v 0 k m sin ⁡ ⁡ ( k m t ) .