With initial conditions $ x(0)= l > 0 $ and $\dot{x}(0)=0$ ,determine the trajectory $x(t)$ of the particle. Also determine its position and velocity at times $$\frac {1}{2}T,\frac {1}{3}T,\frac {1}{4}T$$
Where $$x(t)=a\cos(t\sqrt{k})$$
$$\frac {d^2x}{dt^2} + kx = 0$$ the period $$T=\frac {2\pi}{\sqrt{k}}$$ (I don't know if this is needed)
This is a part of a question and these are all the things I believe are needed