Practising inverse transforms Transform the following functions. In the following, it is understood that we have...
1. problem 2. and 3. as follows Find the inverse Laplace transforms of the following function: 2w7 F(s) = s($2 + 2Cwns + wa) "US 25 (0<5<1) Solve the following differential equation: * + 2wni+wn?x=0, (0) = a, (0) = b where a and b are constants, and 0 << < 1. Solve the following differential equation: ö + 3 + 40 = 2 sint, x(0) = 0, 0) = 0
I need help with these Laplace problems:) (1 point) Find the Laplace transform of <9 f(t) = { 0, " I(t - 9)?, 129 F(s) = (1 point) Find the inverse Laplace transform of e-75 F(s) = 52 – 2s – 15 f(t) = . (Use step(t-c) for uc(t).) (1 point) Find the Laplace transform of 0. f(t) t<5 112 – 10t + 30, 125 F(s) =
Using the inverse transform method... 4.2 Inverse-Transform Method 2, where l < t < 5, Explain how to generate values from a continuous distribution with density function/() = given u E O,1).
7. Find the inverse Laplace Transform of X(so2 with ROC-1< Rels) 1.
find the inverse z transform X(z) = 1-2-3 with [2]<1
One property of Laplace transforms can be expressed in terms of the inverse Laplace transform as dhe >(t) = (- t)" f(t), where f= 4-t{F}. Use this equation to ds" compute 2-1{F} 2 F(s) = arctan 4-1{F}=0
2) Find the inverse z Transform of the following signal: 223-5z2+z+3 X(z) = (z-1)(z-3) [z] <1
Express the following functions in terms of unit step functions and find the Laplace transforms. 2 f(t)= 0 0<ts 1<t<21 t> 21 sint (12 marks)
Express the function below using window and step functions and compute its Laplace transform. 4, 1<t<4 3, 4<t<5 1, 5 t g(t) Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms Express g(t) using window and step functions. Choose the correct answer below. B. gtt) 414) 31145() u(t-5) ○C. g(t) 4111.4(t)+3114.5(t) +110,s(t) O D. g(t)14)+31145t)-u(t-5) Compute the Laplace transform of g(t) Type an expression using s as the variable.)
F One property of Laplace transforms can be expressed in terms of the inverse Laplace transform as L-1 >(t)=(- t)nf(t), wheref=1-1{F}. Use this equation to compute L-1{F}. ds 22 F(s)= arctan Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 1-'{F}=N