Deriving equation of a ramp function graph.

  • Thread starter btbam91
  • Start date
  • #1
btbam91
91
0
Hello, here is my problem.

http://imageshack.us/a/img543/827/rampfunction.png [Broken]

I'm having a little trouble coming up with the function f(t).

I have something like:

f(t) = [(A/T)*t -A] + [(A/T)*(t-2T) -2A] + A*1(t-3T)

Am I on the right track here?

Thanks!
 
Last edited by a moderator:

Answers and Replies

  • #2
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,475
257
f(t) = [(A/T)*t -A] + [(A/T)*(t-2T) -2A] + A*1(t-3T)
This is still a linear equation in [itex]t[/itex], so it can't be right: the graph of any linear function is just a straight line. You will have to use a piecewise definition or perhaps a formula that incorporates unit step functions.
 
  • #3
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,568
774
Have you studied the unit step function ##u(t)##? Expressing your function with it is the best way if you plan to transform the result. For example, if you want your function to equal g(t) on (0,a) and h(t) on (a,b) and 0 elsewhere you would write it like this:$$
f(t) = g(t)u(t) + (h(t) - g(t))u(t-a) + u(t-b)(0-h(t))$$Notice at each term you take out the old formula and put in the new one.
 
  • #4
btbam91
91
0
Thanks for the guidance! I will try to come up with a solution now with this additional knowledge!
 
  • #5
btbam91
91
0
LCKurtz, in trying to follow your formula, I got:

f(t) = [(A/T)*t - A]*u(t) + [((A/T)*t-3A)-((A/T)*t-A)]*u(t-2T)+[(0)-((A/T)*t-3A)]*u(t-3T)

Am I on the right track here?
 
  • #6
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,568
774
LCKurtz, in trying to follow your formula, I got:

f(t) = [(A/T)*t - A]*u(t) + [((A/T)*t-3A)-((A/T)*t-A)]*u(t-2T)+[(0)-((A/T)*t-3A)]*u(t-3T)

Am I on the right track here?

That looks OK.
 

Suggested for: Deriving equation of a ramp function graph.

Replies
2
Views
5K
Replies
4
Views
4K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
21
Views
3K
Replies
8
Views
2K
  • Last Post
Replies
1
Views
5K
Replies
6
Views
1K
Replies
1
Views
4K
Replies
5
Views
2K
Top