simple step function

Oct 2009
24
0
Hi, I just want to make sure I understand the step function.

given that
f(t) =
cost, t < pi
0, t >= pi (>= is my notation for greater than or equal to)

Is the the correct way to write the above in heaviside notation:

f(t) = cost + u_pi_(t)(-cost)

Thanks. Also, does any know of any good resources out there that explain heaviside/step functions? Ive used Pauls Online notes and some youtube videos, just wondering if there are other suggestions out there.
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Hi, I just want to make sure I understand the step function.

given that
f(t) =
cost, t < pi
0, t >= pi (>= is my notation for greater than or equal to)

Is the the correct way to write the above in heaviside notation:

f(t) = cost + u_pi_(t)(-cost)

Thanks. Also, does any know of any good resources out there that explain heaviside/step functions? Ive used Pauls Online notes and some youtube videos, just wondering if there are other suggestions out there.
Yes, it is easy to check that that is correct. If t< pi, then u_pi(t)= 0 so u_pi(t)= 0(-cos(t))= 0 and f(t)= cos(t)+ 0= cos(t). If t> pi, then u_pi(t)= 1 so u_pi(t)(- cos(t))= -cos(t) and f(t)= cos(t)- cos(t)= 0.