- #1

NewtonianAlch

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## Homework Statement

I'm having trouble with part b and part d, where there is some kind of ramp function involved

http://img845.imageshack.us/img845/7507/76500775.jpg

## The Attempt at a Solution

For part b, I calculated the gradient of that ramp, and the intercept which gives y = -x + 4, which would mean it's the function (t - 4)

The other parts of the function are

**2u(t-2)**and

**-2u(t-4)**; which are the rise and fall respectively. So I multiplied

**(t-4)**by these two and it's not the same graph:

**(t-4)*(2u(t-2)-2u(t-4)**

The solutions give

**(t-4)*(u(t-2)-u(t-4)**- which now gives the correct graph. However, I don't understand why since it rises to 2u and drops by 2u, how did the constant two disappear?

Also the equation here is simplified to 2u(t − 2) − r(t − 2) + r(t − 4) - which I do not understand as to where an r came from.

Similarly for part d, I calculate the gradient and intercept, which gives y = -x for the slope, which gives the function

**(-t),**and this shold be multiplied through like

**(-t)(u(t-1) - 2u(t-2))**I would have thought, but once again in the solution that 2 has disappeared from 2u(t-2)

Can someone explain?

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