Problem 8.3: Use LT and another method to find the PS of (x" + α2 x...
Please show all work, thanks. Problem 8.4: Use LT method to find PS of 1 -2 3 -4 x(0) = (1 X'(t)=( Problem 8.4: Use LT method to find PS of 1 -2 3 -4 x(0) = (1 X'(t)=(
(10 points) This problem is related to Problem 8.3 and 8.4 in the text. Consider the function (0 if 0 <t<4 5 if 4 <t<8 f(t) = 3 6 if 8 <t <10 Lo if 10 <t<o. Use the graph of this function to write it in terms of the step function. Use ut - a) for the step function shifted a units horizontally. help f(t) = (formulas) Find the Laplace transform F(s)=L{f(t)} for s + 0. F(s) = C{f(t)}...
Detailed answer with another method then the Laplace transforms Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0...
1270) Refer to the LT table. f(t)=7. Determine tNum,a,b and n. ans:4 1271) Refer to the LT table. f(t)=4t. Determine tNum,a,b and n. ans:4 1272) Refer to the LT table. f(t)=5t^2. Determine tNum,a,b and n. ans:4 1273) Refer to the LT table. f(t)=7exp(3t). Determine tNum,a,b and n. ans:4 1274) Refer to the LT table. f(t)=8(1-exp(3t)). Determine tNum,a,b and n. ans:4 Table of Laplace Transforms le transforms of some common functions are given in Table 36-1. Instead of ansforming a function...
(write After use Laplace Transform to transform the following initial value problem x" + 3x' + 2x=2e-t, x(O) = x'(0)=0, you should get X(s)= S-2 fraction as (S-2)/(S-4)(s+6) for (s-4)(3+6) -). Then, find x(t) = L-2(x(s)= 5 (write 5/6 by 6 -3t e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
part A PART IV. 4. Use the Vibration problem. method of Separation of Variables to find the solution of a String A. Ue (x, t)-0.16us (x, ) 0,0x<8 u(0, t)u(8, t)-0,t0 u(x, 0) = 0 , 0
Solve the given initial value problem using the method of Laplace transforms. y'' + 3y' +2y = tu(t-3); y(0) = 0, y'(0) = 1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Solve the given initial value problem. y(t) = | Properties of Laplace Transforms L{f+g} = £{f} + L{g} L{cf} = CL{f} for any constant £{e atf(t)} (s) = L{f}(s-a) L{f'}(s) = sL{f}(s) – f(0) L{f''}(s) =...
Use Inverse Laplace Transform method and another method to find the partial solution of s y (4)(x) + y(2)(x) = sinx | ly3 (0) = y2)(0) = y(1)(0) = y(0) = 0
QUESTION 3 After use Laplace Transform to transform the following initial value problem X" +x=e-t, x(0) = 1,x'(0) = 1, S-2 you should get X(s)= (write fraction as (S-2)/(5-4)(8+6) for -). Then, find (s-4)(8+6) x(t)= L-?{X(s)}= (write 5/6 by 5 -30 6' e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
1. Solve the system of equations using Laplace Transform(LT): With IV: x(0) 4 With IV :y (0)-5 a. Apply Laplace transform (LT) to the system and solve, by using elimination method, for x(s), and y(s). b. Apply inverse-Laplace transform (L:'T) to the system of s-functions, then solve for x(t), and y(t) 1. Solve the system of equations using Laplace Transform(LT): With IV: x(0) 4 With IV :y (0)-5 a. Apply Laplace transform (LT) to the system and solve, by using...