How do you input piecewise functions into wolfram alpha?
I've tried several approaches, such as defining a function f(t) at certain values, and then using f(t) in my equation, but nothing has worked for me thus far. I love using wolfram alpha, it is an invaluable resource for helping me to better understand my advanced differential equations homework. I am trying to graph a piecewise square wave from 0 to 5pi
The equation is x'' + 2x' + x = f(t) where
__{0, (2n+1)*pi < t < (2n+2)*pi}
f(t) =
__{5, 2n*pi < t < (2n+1)*pi} n = 0,1,2,3,4...etc
f(t) is a square wave with a value of 5 between 0 and pi, then 0 between pi and 2*pi, then 5 between 2*pi and 3*pi... etc. f(t) is the driving function of the ODE. What does the graph look like between 0 < t < 5*pi
Any help inputting this into a plotter, such as wolfram alpha would be greatly appreciated, ty!
Answer
As @ogerard has pointed out you can often input Mathematica expressions to Wolfram Alpha. In your case you may be interested in the SquareWave function. For example, the expression
Plot[2.5 + 2.5 (SquareWave[x/(2 \[Pi])]), {x, -1, 6}]
produces the plot
which, rather unhelpfully, obscures half the graphic along the x-axis.