1. ## (Laplace)Need explainations

hey guys need some explanation on these: the red arrows indicates the part where i do not understand how the eqn derive to the other eqn. (see picture 3)

And maybe if you can also explain the "pattern" of the t>1, 1<t<2, 2<t<4 ...you know what i mean,if the question changes. i am having a problem looking at the "switch" function.
Q1

Q2

Q3

2. Originally Posted by mathsnerd
hey guys need some explanation on these: the red arrows indicates the part where i do not understand how the eqn derive to the other eqn. (see picture 3)

And maybe if you can also explain the "pattern" of the t>1, 1<t<2, 2<t<4 ...you know what i mean,if the question changes. i am having a problem looking at the "switch" function.
Q1

The first of these involves regrouping the terms so:

$\displaystyle (e^{-10t}-e^{-20t})-2(e^{-10(t-2)}-e^{-20(t-2)})=e^{-10t}-2e^{-10(t-2)}-e^{-20t}+2e^{-20(t-2)}$

........ $\displaystyle = (e^{-10t}-2e^{-10(t-2)})-(e^{-20t}-2e^{-20(t-2)})=e^{-10t}(1-2e^{20})-e^{-20t}[1-2e^{-40})$

The second requires that you distribute the derivative over the difference in the
square barckets, then differentiate the exponential terms dependent on t.

RonL

3. Originally Posted by mathsnerd

Q2
for $\displaystyle 1<t<2,\ u(t)=1$, and $\displaystyle u(t-2)=0$

(look up the definition of Heaviside's or the unit step function $\displaystyle u(t)$ if need be).

for $\displaystyle t>2,\ u(t)=1$, and $\displaystyle u(t-2)=1$.

RonL

4. Originally Posted by mathsnerd

Q3
Use: $\displaystyle 30 = \frac{1200}{40}$ then rearrange

RonL

5. Thanks Ron. That was a fast reply.