Undamped, Forced Vibrations amplitude and period

Question

Task says that forced vibration of a point described by second order differential equation: $$x''(t)+x(t)=8\sin{3t}-4\cos4t$$ and initial conditions $x(0)=0; x'(0)=3$. I already have solved this equation. First of all I found solution of homogeneous differential equation $x''+x=0$ and secondly I have found some particular solution. So I get the solution: $$x(t)=\frac{4\cos4t}{15} - \sin3t-\frac{4\cos t}{15}+6\sin t$$ Now, I should find the period and amplitude and really need help with it. I found these formulas: $c=\sqrt{c1+c2}$-amplitude, here $c1=6$ and $c2=\frac{4}{15}$ from the initial conditions and $T=2\pi\sqrt{\frac{m}{k}}$-period, but not sure are they correct in this situation. Please advice. (also here is a graph of displacement vs time. I believe we can see amplitude and period from the graph, but I must calculate it exactly).