Question

I have a function g(t) that I'm trying to describe using unit step function notation. The piecewise definition is: g(t) = t if t <= 8pi, g(t) = 8pi if t > 8pi. So far, I have u_(8*pi)(t) * 8*pi + t and if t <= 8pi, this does equal t but if t is larger then, g(t) equals 8pi + t instead of 8pi. How can I fix this?

Answer 1

so far you have\[8\pi\large u_{8\pi}(t)+t\]we need a switch that will undo the t that we have added
the inverse of addition being subtraction we have\[\large g(t)=8\pi u_{8\pi}(t)+t-tu_{8\pi}(t)=t+(8\pi-t)u_{8\pi}(t)\]