The above pictured function can be defined using Heaviside step functions as
The above pictured function can be defined using Heaviside step functions as
The solution to $$\displaystyle{\ddot x x = 1-u_{2\pi}(t)}$$, with $$x(0)=1$$ and $$\dot x(0)=0$$ is given by
The solution to $$\displaystyle{\ddot x x = \delta(t) - \delta(t-2\pi)}$$, with $$x(0)=1$$ and $$\dot x(0)=0$$ is given by