This applet graphs several solutions to the DE \(\dot{y} + ky = f\). Here we will call \(f\) the input and \(y\) the response of the system. The value of \(k\) is settable using the \(k\) slider.

Graphs
There are four color coded graphs.

• \(f_h\) is the periodic box driver.
• \(y_r\) is the response to input \(f_h\) from the (pre) initial condition \(y(0-) = y_0\). (If \(h \gt 0\) pre and post initial conditions are the same.)
• \(y_p\) is the periodic response to \(f_h\).
• \(y_i\) is the response to the period \(1\) unit impulse train from the pre-initial condition \(y(0-) = y_0\).

Sliders

• The \(h\) and \(k\) sliders set the values of the parameters \(h\) and \(k\).
• The \(y_0\) slider sets the initial condition.

© 2013-2017 J. Orloff, H. Miller, J. Claus