Download EEL 3105 Fall 2011 - Laplace Transforms & Diff. Equations: Practice Set 3 - Prof. Pramod P and more Exams Electrical and Electronics Engineering in PDF only on Docsity!
EEL 3105 Fall 2011
Practice Problem Set 3
- Find Laplace transform of
f t ( ) 7 U t ( 4) 4 ( t 2) 3sin(6 t / 4)
Here U(t) is the unit step function, (t) is the unit impulse function.
- Find inverse Laplace transform for the following functions: a. F(s) = 2 2 ( 2 9)
s s s s
b. F(s) = 2 2 2 ( 2 9)
e s^ s s s s
- Consider the differential equation 2 2 5 10 3 8
d y dy (^) y du u dt dt dt
Find the transfer function H(s)= ( ). ( )
Y s U s
- Consider the differential equation 2 2 5 10 3 8
d y dy (^) y du u dt dt dt
Find A, B, C for a state‐space representation of the form
dx (^) Ax t Bu t dt y t Cx t
- Consider the differential equation 3 2 3 2 9 0.
d y d y dy dt dt dt
We are given that y(t)=4e‐3t^ is a solution to this differential equation. Find the value of .
- Consider the differential equation 2 2 4 16 ( ).
d y dy (^) y u t dt dt
Suppose u=unit impulse function and y(0)=0, dy/dt(0)=0. Find y(t). You can use any method to solve this problem.
- Consider the differential equation
dy (^) 3 ( ) y t u t ( ). dt
Suppose u(t) is the unit step function. Calculate
lim (^) t y t ( ).
- Consider the linear differential equation 1 1 1 ...^1 ( )^ ( ).
n n n n n^ n
d y d y dy (^) y t u t dt dt dt
(^) (^)
Suppose all initial conditions are zero and the suppose the unit step response is given by
y ( ) t 5sin(3 ). t
With zero initial conditions and u(t)=unit impulse function, find the solution y(t).
Useful Laplace transform rules:
2 2 2 2 LT (sin( t )) , LT (cos( t )) s , LT e ( t )^1 s s s
^
If LT ( f t ( )) F s ( ),then LT e ( ^ ^ t^ f t ( )) F s ( ), LT ( f t ( h )) e hsF s ( ).
