Given the function begin{cases}e^{-t}& text{if } 0leq t<2 0&text{if } 2leq tend{cases}Express f(t) in terms of the shifted unit step function u(t -a)F(t)

Caelan 2020-11-08 Answered

Given the function {etif 0t<20if 2t
Express f(t) in terms of the shifted unit step function u(t -a)
F(t) - ?
Now find the Laplace transform F(s) of f(t)
F(s) - ?

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

escumantsu
Answered 2020-11-09 Author has 98 answers

Step 1
Since f(t)=0 for 2t and t<0 so create step function: u(t)u(t2) which will give those zero values.
Thus, f(t)=et[u(t)u(t2)] or f(t)=etu(t)etu(t2)
Step 2
Calculate Laplace transform:
F(s)=f(t)estdt
=(etu(t)etu(t2))estdt
=(etu(t))estdt(etu(t2))estdt
=0e(s+1)tdt2e(s+1)tdt
=1(s+1)e2(s+1)(s+1)
=1e2(s+1)(s+1)
Step 3
Thus, Laplace transform is F(s)=1e2(s+1)(s+1)

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2022-05-17
Let
[ 2 1 0 0 2 1 0 0 2 ]
and
| x ( t ) | = ( x 1 2 ( t ) + x 2 2 ( t ) + x 3 2 ( t ) ) 1 / 2
Then any solution of the first order system of the ordinary differential equation
{ x ( t ) = A x ( t ) x ( 0 ) = x 0
satisfies
1. lim t | x ( t ) | = 0
2. lim t | x ( t ) | =
3. lim t | x ( t ) | = 2
4. lim t | x ( t ) | = 12
asked 2020-11-27

Solve differential equation dxdy+xy=11+y2

asked 2022-05-21
g ( x ) is continuous on [ 1 , 2 ] such that g ( 1 ) = 0 and
g ( x ) x 2 = 1 g 2 ( x )
Find g ( 2 )
I found that g ( x ) = sin ( c 1 x ) and since g ( 1 ) = 0 shouldn't my c be equal to 1, so that sin ( 1 1 ) = 0.
But when I try for g ( 2 ) with c = 1, I am getting a different answer from the textbook.
asked 2021-02-13
Solve differential equation dy/dx12x3y=x3
asked 2022-01-19
The Runge Kutta method is known as:
a. An analytical method of solving first order differential equations.
b. An accurate method of solving first order differential equations.
c. A numberical method of solving first order differential equations.
d. A complex method of solving first order differential equations.
asked 2022-02-16
y+eyx=0
that I have simplified like so
ey=xy
lney=ln(xy)
y=ln(xy)
but I do not know how to solve this further to obtain the general solution. I have done first order linear differential equation strategies so far. How should I get about doing this question with the strategies I have?
asked 2021-03-02

Transform the given initial value problem into an initial value problem for two first-order quations u"+0.25u+4u=2cos(3t), u(0)=1,u(0)=2