please show all your work. Thank you. 1. Given that L{sin t} = (52+1)(52+9) evalu evaluate...
1. Basic properties of Laplace transforms: Show all of your steps. You can use tables of Laplace transforms to assist with the calculations. (a) Using a table of Laplace transforms, evaluate L {2t3 - 3e-2 t (b) Evaluate the Laplace transform of t2 sin(bt). d2 ds2 Hint: First verify the identity estt2 f(t)dt = estf(t)dt
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5.5 EXERCISES 1-6 Evaluate the integral by making the given substitution. 1. cos 2x dx, u= 2x 2. | xe dx, u = -x x3 + 1 dx, u= x + 1 sin cos e de, u = sin e - dx, u=x4 - 5
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A voltage (in volts) is given by u(t) 12 cos 200t-5 sin 200t Express the voltage as (a) a cosine function and (b) a sine function.
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(1 point) Use Laplace transforms to solve the integral equation y(t) – v yết – U) do = 4. The first step is to apply the Laplace transform and solve for Y(s) = L(y(t)) Y(s) = Next apply the inverse Laplace transform to obtain y(t) y(t) =
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1. Solve the following Laplace Transform problems: (a) (20 points) Given the following function f(t) = [10+ (4e-2+ + 3te-4t)e2t]u(t) A Find F(s) = C[f(t) as a proper rational function. F(8) must be in fully factored form. (b) (20 points) Let: f(t) = Ś(n + 2)!e=n(+36)(t – 3n) Find F(s) = [f(t) as a proper rational function.
HI, PLEASE ANSWER ALL PARTS AND PLEASE SHOW ALL WORKINGS STEP BY STEP. THANK YOU. Question 1: a) Show from first principles that the Laplace transform of the function f(n)=1, 120 is f(s) = Make a note of any conditions imposed on the transform variable "s" to ensure the transform exists. (8 Marks) b) Find, using the appropriate theorem, the Laplace transform of a function f(t); b) f(t) = t.sin(56) OR ii) f(t) = 5 sin 2(t - 3). H(t...
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Consider the following game in strategic form 2 L M R 1 2, 2 U 1,1 1,3 1, -1 3, 0 3, -3 (i) Find the safety level and the maximinimizing strategy of each player Find all Nash equilibrium points of this game (ii)
Differential equation
Q5 please
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Q10 if possible, thank you so much
Exercises 1. Show that L{cos kt) = s22 for s> 0. 2. Euler's formula elkcos kt+i sin kt can be used to obtain an additional formula cos kt(ek+e-ik), Show that the result of Exercise 1 can now be obtained with a formal application of the Laplace transform. 3. Obtain the transform for sin kt by an argument similar to the one suggested in Exercise 2 4. Evaluate L(r2...
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Question 14 5 pts Use the Laplace transform to solve the given initial-value problem. y" + 4y=f(t – 2), y(0) = 1, y (0) = 0 Oy(t) = cos(2t) + U (t – 2) · sin[2(t – 2)] Oy(t) = {U (t – 2) sin(2t) Oy(t) = {U (t – 2) sin(2(t – 2)] Oy(t) = cos(2t) + U (t – 2) sin(2t)
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3. Plot the following signals: a) 9.(t) = 11(2t+5) b) 92(t) = sgn(2t) - sgn(t)