If y " +2y +2y = 3t2, y (0) = 0, y (0) = 2, what is the Laplacetransform of y?2s6.$2+2s+2g8 (8² +28+2)g° (s² +2s+2)2+.s4 (s²+2s+2)s2+2s+22s2 +2s+2go (3² +2s+2)తొలి

Answered: Image /qna-images/answer/298ffa69-0fc6-49d4-b3c3-db64e3d2a7aa.jpg

Answered: If y " +2y + 2y = 3t2, y (0) = 0, y (0)…

Engineering

Mechanical Engineering

If y " +2y + 2y = 3t2, y (0) = 0, y (0) = 2, what is the Laplace transform of y?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: Determine the Laplace Transform of the following functions. Show your detailed solutions. 1. t cos t

A: ft=tcost

Q: Calculate the particular solution to the forced differential equation x"+ 3x = Scos(2r)

A: Given differential equation, x''+3x = 5cos2t

Q: Solve for the laplace transform using the formula G(t) = t5 –e-9t + 5(t – 1)²

Q: Derive the z-transform for f(t) = sin cot u(t).

A: ft=sin ωt u(t) We can write sin ωt=ejwt-e-jwt2j x(z)=∑ n=-∞n=∞f(t)z-t since it is unit step x(z)=∑…

Q: Question The Laplace transform of f (t) = 5cos (7t) – 7e2t + 2t³ is: F(6) =++을 2 %3D s²+4 s+3 )

Q: Find the inverse Laplace transform of the given function. 2! F(s) = (s – 6)³ L-'{F(s)} =

Q: FIND INVERSE LAPLACE TRANSFORM, USE THE LAPLACE OF INTEGRALS | 4 5s (s2+4). 8.

A: Find the inverse laplace of the function.

Q: The path of a moving point Pis defined by the equation y=60-(x³/3). The displacement of the point…

A: Given: The path of the moving point is defined by the equation y=60-x3/3. The displacement of…

Q: For Numbers 3-5. Solve the Laplace transform of the following using the formula. 3. F(t) = e-2t-5 4.…

Q: The Laplace Transform of : cosh(3t)+2sin(5t) is

Q: Use the table of Laplace transforms to find the Laplace transform of each of the following. 2. (a)…

Q: Use the inverse transforms of some basic functions to find the given inverse transform. L f(t) =

Q: t sinh 6t 1.6 f(1)='

A: Given f(t) = (t sinh 6t)/t2 This can also be write as f(t) = sinh 6t/t (1)…

Q: Find the Laplace transform of the given function; b is a real constant. f(t) = cos(bt) %3| Your…

Q: 2. Use the laplace transform to solve for f(t) of the given differential equation. (10 pts) dx (0) =…

Q: 2. f(t) = cos25t %3D

A: find the laplace transform of the function.

Q: d²y(t) dy(0) = 20u(t) y(0) = 25; dt dt2

Q: 95 Solve the following inverse transform Laplace transformations. 7s +15 8² +2

A: As per our guidelines we are supposed to answer only one question in case of multiple questions…

Q: Solve for the Laplace transform of the function below: f(t) ↑ 1 t 1

A: From the given graph, the function is a straight line passing through points (1,0) and (0,1), when t…

Q: Determine the inverse Laplace transform of the function: F(s) 7s-41s+84 (s-1)(s2 4s+13)

Q: Calculate the Inverse Laplace transform of the following. Please write down all the steps of your…

A: Laplace transform concept is basically used in many mechanical control system devices. First partial…

Q: • Find the Laplace Transform below a) L{2} b) L'e=} nefsinh Llos 2} c) L{t} d) Lt'} 3 k) L{sin 2t}…

A: To Find : The laplace transform. Formula used: L{1}=1sL{eat}=1s-a L{tn}=n!sn+1 L{cosat}=ss2+a2…

Q: Use the definition of the Laplace transform to determine the Laplace transform L[ƒ(t)](s) of the…

Q: • Find the Laplace Transform using the Laplace Transform Pairs and the Laplace of derivatives: 4. y…

A: Following is the answer for the question.

Q: The Inverse Laplace Transform for 5/3S - 2/ ((3(s+3)) is

A: According to the details provided in the question, we need to calculate inverse Laplace transform.

Q: QUESTION 9 Consider the inverse Laplace transforms: s- a at cos(bt) ((s - a)² + 6² = ecos(bt) and b…

Q: s+1 The inverse Laplace transform of the function is s3 +s2-6s

Q: What is the laplace transform of f(t)= -4e¯3t? 4 s-3 -4 s+3 -4 s-3 4 s+3

A: Option 2 is correct -4/(s+3)

Q: Example: Find Laplace transform of function: 1 F(s) %D (s + 1)(s² + 4)

Q: Find the inverse Laplace transform L-1{F(s)} of the function 10 F(s) : (s – 4)3 NOTE: The answer…

Q: The Laplace transform of f (t) = e-3t cos(2t) + 2te3t is:

A: L{e-3tcos(2t) + 2te3t} = L {e-3tcos(2t)} + L{2te3t} = s+3(s+3)2+22+ 2 {(-1)n dndsnn(s-a)n+1} =…

Q: Use the inverse transforms of some basic functions to find the given inverse transform. S s2 + 4s

Q: Where the general equation of vibration is (NIKI = w*[M][X]. Find eigenvalues and eigenvectors. Q.3.…

Q: Find the inverse Laplace transforms 10s s²+100 3s s²+7s

A: L-110ss2+100=L-110ss2+102 =L-110.ss2+102…

Q: 4. The Laplace transform 5 3²+4s+6 can be expressed as L{e¹[qssin(96t) +97cos(* * 1)]}

A: The function is F(s)=5s2+4s+6 The inverse Laplace function formula used is…

Q: Solve the Inverse Laplace Transforms 3s +8 (82 + 28 + 5 ,

A: L-13s+ 8s2+ 2s+ 5

Q: Q. 2 Find Laplace Transform of: 1 1 2

A: The given curve represents the function fx. Write the value of the function fx for the domain. fx=x…

Q: Solve the initial value problem below using the method of Laplace transforms. у" - у'- 30у %3D 0,…

Q: Find the inverse Laplace transform L-{F(s)} of the given function. 8s2 – 28s + 294 F(s) = s(s² + 49)…

Q: 1. As we discussed in class try to develop a homogeneous transform H from frame 1 to frame 2, by…

A: Here the above sum can be done by calculating the materix of frame

Q: Use the standard list of Laplace Transform and determine the following: a) L{1+ 2t –t*} 3 b) L{5e2t…

Q: Find the Laplace transform for (a) f(t) = t cosh 2t. (b) f(t) = e-2t cos 2t.

A: The stepwise procedure to solve this Laplace transform is shown in the following attached image:

Q: H(s) = s3-4s² +6s+17 S4-2s3-s²+2s

Q: Write, but do not solve, the Laplace transform of the equations of motion for the system shown in…

Q: 1 E. Find the inverse Laplace transform for F(s)= S (S (s² – 4)

Q: Calculate the Inverse Laplace transform of the following. Please write d Il the steps of your…

Q: Compute theresponse x(t) for the following driven, undamped oscillator using the Laplace transform…

Q: QUESTION 2 Use the inverse transforms of some basic functions to find the given inverse transform.…

Q: Find the transform of the given function of s. 3s + 8 F(s) s2+ 8s + 20 (A) f =e 4t (3 cos 2t - 2 sin…

A: The Laplace transform of F(s)=3s+8s2+8s+20 is L-1{3s+8s2+8s+20}=f(t)=e-4t (3 cos 2t - 2 sin 2t).…

Q: Find the Laplace Transforms of the following function: t<0 f(t) = e-at t20 Note: The scanned…

A: Given f(t)=0 t<0t2e-a.t t≥0

Concept explainers

Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

100%

If y " +2y +2y = 3t2, y (0) = 0, y (0) = 2, what is the Laplace
transform of y?
2s
6.
$2+2s+2
g8 (8² +28+2)
g° (s² +2s+2)
2
+.
s4 (s²+2s+2)
s2+2s+2
2
s2 +2s+2
go (3² +2s+2)
తొలి

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Q1: * Q1 Calculate The Inverse Of The Matrix: [4 A= 2 -2 11 4 4 3 1 Add file Q2: * Using Green's theorem, evaluate the line integral (y- a)dr- (x +y°)dy, where the contour C encloses the sector of the circle with radius a lying in the first quadrant 0 = 1/2 R >-0 a
Copy of Based on the kinematic system below If we rotate (A-B) 90 degrees counter-clockwise, and (B-P) 90 degrees clockwise where will be the point P y (2,4) Kinematic skeleton 42) O (4,4) (4,6) (6,4) O (6,6)
[(<+1) (x-5) 7 2 3 -5 I. IF A and B = = %3D 6 7 -- -2X (2x+1 Find the values of x if AB = 25 8.
Solve the system of linear equations. x+y+z = -6 x-6y-7z = -29 -7y-5z = 4 O (-8, -7,9) O (-6, -7, 10) O (-7,-8, 9) O (-7,-6, 10) O (9,-7,-8)
Solve the following for x: 6log. Vx-log,3x=log, x i1) 32-5 =27 i11) Vx +x+10 =x+2
$+2.5$41 543834 2 8 b. A student has written a mathematical model for a rotational mechanical system without gears and some data were missing as shown below: [4s² + 2s +5 -25 as 0 -2s 3s² + 4s +6 -(1+B) 0 -6 3s +6 [0₁(s)] 0₂ (s 03(s)] What are the values of a and B? 2. What is the degree of freedom of the system? Sketch the expected rotational mechanical system and show thetorque, angular displacements and all values of inertias, springs, and dampers on the sketch with 85²2445445+8 their units. (89² +2+5+8) (33+4)
= Find the general solution to the following 2nd Order O.D.E., where y" y" + y + y = 0 (³x) - ₂ - C₂ sin sin (√³7)} ○ y(x) = e. {c₁ cos (³0) - -x)+ + C₂ sin(x)} y(x) = e{c₁ cos y(x) = e{c₁ cos(x) + ₂ sin(x)} ○ y (x) = c₁ · e¯7 · cos (³x) + c₂ · ež · sin (√³x) ○ y(x) = c₁ ·e· cos(x) + c₂ · €¯ · sin (³x) d² y(x) dx²
write vector loop equation(s) theta2=57 also if a new length is constructed find its value. 02 57° 30° X L₁= 162 L2=40 L4=122 L3=96 0₁
To create AutoCAD Q: Use the principle of the geometric model shown in the following figure? R8 16 22 50 015 50 425 40 80 20 r
Determine if the system is consistent or inconsistent. Justify your answer and find all solutions to the system of linear equations. Justification should be written on your solution paper. Transform the matrix into ROW ECHELON FORM (REF) using row operations. 2x +8y+ 6z = 20 4x+2y-2z =-2 3x-y+z = 11 Enter final answer: (x, y, z) =(
Given: N1 = 10, N2 = 20, N3 = 30, N4 = 40 J1 = 1, J2 = 2, J3 = 3, J4 = 4, J5 = 5, D1 = 1, and D2 = 2 Determine: 01(s)/Tl(s) T₁(1) 0₁ (1) CC N₂ D2, J2 N₁ J₁. Di N3 J3 N4 N₂0 JS J4
The figure shows a function generator linkage in which the motion of rocker 2 corresponds to x and the motion of rocker 4 to the function y=f(x). Use three precision points and chebychev spacing and synthesize the linkage to generate the following function. y = 4cos (-x) 0