Exercise 1.6: Harmonic oscillator

The two coupled first order equations

$$\frac{dy}{dt}=p; \frac{dp}{dt}=-4\pi ^2 y$$

define a harmonic oscillator with period $T=1$. Compute the position $y$ and momentum $p$ as a function of time using a generalization of the previous code. Plot the results for $y_0=1$ and $p_0$=0. Investigate the accuracy with which the system returns to the initial state at integral values of $t$.

Figure 2: Object in a two dimensional trajectory under the effect of gravitational and dragging forces