Obtain the transfer function of the system if y(t)=e^{-t}-2e^{-2t}+e^{-3t} text{ and } x(t)=e^{-0.5t}

smileycellist2 2020-11-26 Answered
Obtain the transfer function of the system if y(t)=et2e2t+e3t and x(t)=e0.5t
You can still ask an expert for help

Want to know more about Laplace transform?

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

lobeflepnoumni
Answered 2020-11-27 Author has 99 answers
Step 1
Laplace transform of eat is 1(s+a) Thus, Laplace transform
ofy(t)=et2e2t+e3t is :
Y(s)=1(s+1)21(s+2)+1(s+3)
=(s+2)(s+3)2(s+1)(s+3)+(s+1)(s+2)(s+1)(s+2)(s+3)
=(66+2)(s+1)(s+2)(s+3)
=2(s+1)(s+2)(s+3)
Step 2
Also, Laplace transform of x(t)=e0.5t is: 
X(s)=1(s+0.5)
Step 3
Thus transfer function is: (Y(s))(X(s))=2(s+1)(s+2)(s+3)1(s+0.5)
=2s+1(s+1)(s+2)(s+3)
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 2021-05-03
When talking about boundary conditions for partial Differential equations, what does an open boundary mean?
asked 2022-01-21
Solve the differential equation y=|x|,y(1)=2
asked 2021-09-19
Find the inverse Laplace transform of the following transfer function:
Y(s)U(s)=50(s+7)2+25
Select one:
a)f(t)=10e7tsin(5t)
b)f(t)=10e7tsin(5t)
c)f(t)=50e7tsin(5t)
d)f(t)=2e7tsin(5t)
asked 2021-09-16
Find the solution of the given system of differential equations by Operator method or Laplace transform.
2dxdt+dydt+x+5y=4t
dxdt+dydt+2x+2y=2
x(0)=3,y(0)=4
asked 2020-11-29
Find the Laplace transform of f(t)=tetsin(2t)
Then you obtain F(s)=4s+a((s+1)2+4)2
Please type in a = ?
asked 2022-01-18
I have the following equation
(xy2+x)dx+(yx2+y)dy=0
and I am told it is separable, but not knowing how that is, I went ahead and solved it using the Exact method.
Let M=xy2+x and N=yx2+y
My=2xy and Nx=2xy
M.dxxy2+x=x2y2+x22+g(y)
Partial of (x2y2+x22+g(y))xy2+g(y)
g(y)=y
g(y)=y22
the general solution then is
C=x2y22+x22+y22
Is this solution the same I would get if I had taken the Separate Equations route?
asked 2020-10-28
Solve both
a)using the integral definition , find the convolution
fg of f(t)=cos2t,g(t)=et
b) Using above answer , find the Laplace Transform of f*g