Find the Laplace Transform via the graph (won't let me upload the graph). In the Y...
Find the Laplace Transform via the graph (won't let me upload the graph). In the Y direction it goes to 12, in the X the period is 4a. In this period, it linearly increases from 0 to 12. This repeats for every subsequent period of length 4a.
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Find the Laplace Transform via the graph (won't let me upload
the graph). In the Y...
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform...
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform 10<tsI g(t) = le-3, +1 , 1<t 2 .22 Q2 Use Laplace transform to solve the following initial value problem: yty(o)-0 and y (0)-2 A function f(x) is periodic of period 2π and is defined by Q3 Sketch the graph of f(x) from x-2t to2 and prove that 2sinh π11 f(x)- Q4 Consider the function f(x)=2x, 0<x<1 Find the a Fourier cosine series b)...
Question 2: (26 marks) 2.1 Find the The Laplace transform of the following function t, if...
Question 2: (26 marks) 2.1 Find the The Laplace transform of the following function t, if 03t<1 2t, if t1 [3] 2.2 Find the inverse Laplace transform of 10e 2 52 - 53 +632 - 25 + 5 (10] 2.3 Find y(4) if y(t) = u(t){t - 2)2 - us(t)/(t - 3) - 2) - us(t)e' (51 2.4 Solve the following initial value problem given by y" + 4y = 28.(t) (0)=1/(0) = 0 181 Question 3: (17 marks) Let...
Chapter 5, Section 5.2, Question 24 Find the Laplace transform Y (s) -Ifyj of the solution...
Chapter 5, Section 5.2, Question 24 Find the Laplace transform Y (s) -Ifyj of the solution of the given initial value problem. y(0)=0, y'(0)=0 , 0, î t <x The Laplace transform of the solution y of the initial value problem is !(y) = Y(s) = Click here to enter or edit your answer
Use Inverse Laplace Transform method and another method to find the partial solution of s y...
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
I need help with d and h. Thank you. 24.1. Find the Laplace transform Y(s) of...
I need help with d and h. Thank
you.
24.1. Find the Laplace transform Y(s) of the solution to each of the following initial-value problems. Just find Y (s) using the ideas illustrated in examples 24.1 and 24.2. Do NOT solve the problem using methods developed before we started discussing Laplace transforms and then computing the transform! Also, do not attempt to recover y(t) from each Y(s) you obtain. Yle y' + 4y = 0, with y(0) = 3 Y...
1 1 1111 ... Question 2 2.1 Find the Laplace transform for 1, DCICI (-1.11s f(x...
1 1 1111 ... Question 2 2.1 Find the Laplace transform for 1, DCICI (-1.11s f(x + 2n)-f(x) VcZ. 2.2 Compute sis:+4) 2.2.3-1 74-1 2.3 Suppose we have a beam of length 1 simply supported at the ends and suppose that force F - 1 is applied at 8 – in the downward direction. Suppose that 1:1 = 1 for simplicity. Find the beam deflection y(x). 2
1. (10 points) Find the inverse Laplace transform of the following: 85 - 4s +12 s?...
1. (10 points) Find the inverse Laplace transform of the following: 85 - 4s +12 s? +45-5 b. F(x) = s(s? +2s + 5) 2. (10 points) Determine if the following differential equation is exact. Be sure give a reason for why or why not. If it is exact, solve it. (xy? + 3x y)+(x° +xºy)y'=0 a. F(s)= (1-25)e-
find the general solution (y) using laplace transform (1 point) Consider a spring attached to a...
find the general solution (y) using laplace transform
(1 point) Consider a spring attached to a 1 kg mass, damping constant 8 = 5, and spring constant k = 6 The initial position of the spring is 4 metres beyond its resting length, and the initial velocity is -9 m/s. After 1 second, a constant force of 12 Newtons is applied to the system for exactly 2 seconds Set up a differential equation for the position of the spring y...
Ry 82. Let f(x, y) - 0 if (x, y)-0 The graph of f is shown on page 813. a. Show that j x,0) - x f...
ry 82. Let f(x, y) - 0 if (x, y)-0 The graph of f is shown on page 813. a. Show that j x,0) - x for all x, and a0, y) y for all y. b. Show that (0, 0) ахау (0, 0) The three-dimensional Laplace equation dy dx is satisfied by steady-state temperature distributions T-f(x, y, z) in space, by gravitational potentials, and by electrostatic poten- tials. The two-dimensional Laplace equation ar'ду obtained by dropping the a2f/az2 term...
(1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C...
Please solve these three questions!
(1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C1 function g : [a, b - IR. Show that the path integral of a continuous function f: IR2- R over the path C is b) Let g : [a, b] - IR be a piecewise C1 function. The length of the graph of g on (t, g(t)). Show that [a,b]...
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform 10<tsI g(t) = le-3, +1 , 1<t 2 .22 Q2 Use Laplace transform to solve the following initial value problem: yty(o)-0 and y (0)-2 A function f(x) is periodic of period 2π and is defined by Q3 Sketch the graph of f(x) from x-2t to2 and prove that 2sinh π11 f(x)- Q4 Consider the function f(x)=2x, 0<x<1 Find the a Fourier cosine series b)...
Question 2: (26 marks) 2.1 Find the The Laplace transform of the following function t, if 03t<1 2t, if t1 [3] 2.2 Find the inverse Laplace transform of 10e 2 52 - 53 +632 - 25 + 5 (10] 2.3 Find y(4) if y(t) = u(t){t - 2)2 - us(t)/(t - 3) - 2) - us(t)e' (51 2.4 Solve the following initial value problem given by y" + 4y = 28.(t) (0)=1/(0) = 0 181 Question 3: (17 marks) Let...
Chapter 5, Section 5.2, Question 24 Find the Laplace transform Y (s) -Ifyj of the solution of the given initial value problem. y(0)=0, y'(0)=0 , 0, î t <x The Laplace transform of the solution y of the initial value problem is !(y) = Y(s) = Click here to enter or edit your answer
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
I need help with d and h. Thank
you.
24.1. Find the Laplace transform Y(s) of the solution to each of the following initial-value problems. Just find Y (s) using the ideas illustrated in examples 24.1 and 24.2. Do NOT solve the problem using methods developed before we started discussing Laplace transforms and then computing the transform! Also, do not attempt to recover y(t) from each Y(s) you obtain. Yle y' + 4y = 0, with y(0) = 3 Y...
1 1 1111 ... Question 2 2.1 Find the Laplace transform for 1, DCICI (-1.11s f(x + 2n)-f(x) VcZ. 2.2 Compute sis:+4) 2.2.3-1 74-1 2.3 Suppose we have a beam of length 1 simply supported at the ends and suppose that force F - 1 is applied at 8 – in the downward direction. Suppose that 1:1 = 1 for simplicity. Find the beam deflection y(x). 2
1. (10 points) Find the inverse Laplace transform of the following: 85 - 4s +12 s? +45-5 b. F(x) = s(s? +2s + 5) 2. (10 points) Determine if the following differential equation is exact. Be sure give a reason for why or why not. If it is exact, solve it. (xy? + 3x y)+(x° +xºy)y'=0 a. F(s)= (1-25)e-
find the general solution (y) using laplace transform
(1 point) Consider a spring attached to a 1 kg mass, damping constant 8 = 5, and spring constant k = 6 The initial position of the spring is 4 metres beyond its resting length, and the initial velocity is -9 m/s. After 1 second, a constant force of 12 Newtons is applied to the system for exactly 2 seconds Set up a differential equation for the position of the spring y...
ry 82. Let f(x, y) - 0 if (x, y)-0 The graph of f is shown on page 813. a. Show that j x,0) - x for all x, and a0, y) y for all y. b. Show that (0, 0) ахау (0, 0) The three-dimensional Laplace equation dy dx is satisfied by steady-state temperature distributions T-f(x, y, z) in space, by gravitational potentials, and by electrostatic poten- tials. The two-dimensional Laplace equation ar'ду obtained by dropping the a2f/az2 term...
Please solve these three questions!
(1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C1 function g : [a, b - IR. Show that the path integral of a continuous function f: IR2- R over the path C is b) Let g : [a, b] - IR be a piecewise C1 function. The length of the graph of g on (t, g(t)). Show that [a,b]...
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