The subject is differential equations 0<t 11. Use Table 5.1 to find Laplace transform for the fiunction fO). 0 t l), f(t) = 3 [h(t-1 )-h(t-4)]
differential equations
Definition 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral 00 L{f(t)} = -192 e-stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. 16, f(t) = {6, ost<4 t24 Complete the integral(s) that defines L{f(t)}. L{f(t)} = Datet (" dt Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0)
differential
equations
Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral **F¢)} = [" e stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. 16, f(t) = Ost<4 t24 Complete the integral(s) that defines {f(t)}. {f(t)} = o Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0)
Use the Laplace transform to solve the given system of
differential equations.
Use the Laplace transform to solve the given system of differential equations. of + x - x + y = 0 dx + dy + 2y = 0 x(0) = 0, y(0) = 1 Hint: You will need to complete the square and use the 1st translation theorem when solving this problem. x(t) = y(t) =
Differential equations 7.4 Operational properties II
Formula to use
Use operational properties of the Laplace Transform to determine L{f(x)}, where f(x) is represented in the graph below. Simplify your answer. f(t) 4 1 1 2 3 4 THEOREM 7.4.3 Transform of a Periodic Function If f(t) is piecewise continuous on [0, 0), of exponential order, and periodic with period T, then 1 L{f(t)} es f(t) dt. () di. 1 - e-ST
Differential Equations
Please use the LaPlace Transform method
USE LAPLACE TRANSFORM ME 7700 TO solve the following ... 2 ас 11 sint <0,05 (3) 3 -34 t e 3° +6° + 7, <0,05
4. Solve the given differential equation (i.e., find y(t)) using Laplace transform method: and subject to the conditions that yo) = 0 and y” + 2y'+y=0 y’0) = -2. 21
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
Problem 3.a. (4 pt) Find the Laplace transform of f(t) = | 1, for 0 <t<1 5, for 1 <t< 2 le-t for t > 2
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
Find the Laplace transform of f(t)={ 0, t<4 (t-4)3, t≥4 F(s)=