[3] [6 POINTS] Using the definition of the Laplace transform, find the Laplace transform of the...
1. (2 points) Using the definition, find the Laplace Transform of the function: e21, 0<t<3 f(t) = 3<t
2. Consider the function 3 I < (a) Find the Laplace transform of f by direetly using the integral definition of a Laplace transform. (b) Write f in es of step functions, and use the t-shiting theorem to find the Laplace transform of f. (c) Use MATLAB to find the Laplace transform of f
3. [-13 Points) DETAILS ZILLDIFFEQ9 7.1.007. -Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t2 0. Then the integral 2100) - 6 *e=4) dt is said to be the Laplace transform of f, provided that the integral converges. Find {{f(t)}. (Write your answer as a function of s.) L{f(t)} (s > 0) f(t) (2, 2) Need Help? Read it Talk to Tutor
Using the definition of the Laplace Transform, and proper notation, find the Laplace transform of fle=10,0<t<2 7,122
Question (2): Laplace Transformsa) Find the Laplace Transform of the following using the Laplace Transform table provided in the back:$$ f(t)=\frac{1}{4}\left(3 e^{-2 t}-8 e^{-4 t}+9 e^{-6 t}\right) u(t) $$b) Find the inverse Laplace Transform \(F(s)\) of the following function \(f(t)\) using the table:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
Find the Laplace transform using the definition of Laplace cos2 4t
Find the Laplace transform using the definition of Laplace cos2 4t
please solve and explain each step 1. (15 points) Find the Laplace transform using the definition of Laplace cos2 4t Explain each step for full credit.
Find Laplace transform of ?(?) = 2 + 5? Find Laplace transform of ?(?) = 2?-t + 3??-4t Find time function corresponding to this Laplace transform: ?(?) = (2s2+s+1)/(s3-1) Solve this ODE using Laplace transform : ?̈(?)+2?̇(?)+4?(?)=0; ?(0)=1, ?̇(0)=2 Solve this ODE using the Laplace transform : ?̈(?)−2?̇(?)+3?(?)=0; ?(0)=2, ?̇(0)=1
1. Obtain Laplace transform of the following functions using the Laplace transform definition a. x(t)-sin!) b. x(t)-t