### Question #4 (chapter La Place Transform, online)Solve $ Y'' + Y = \sin(2t) $ using Laplace and inverse Laplace transforms.---### Question 5(Use the electrical circuit differential equation - Book reference section 16.3)\[\frac{d^2 q}{dt^2} + \left( \frac{R}{L} \right) \frac{dq}{dt} + \left( \frac{1}{LC} \right) q = \left( \frac{1}{L} \right) E(t)\]Where:- $ R $ is the resistance (in ohms),- $ C $ is the capacitance (in farads),- $ L $ is the inductance (in henrys),- $ E(t) $ is the electromotive force (in volts),- $ q $ is the charge on the capacitor (in coulombs).Find the charge $ q $ as a function of time $ t $ for the electrical circuit described. Assume that $ q(0) = 0 $ and $ q'(0) = 0 $.Given values:- $ R = 20 $- $ C = 0.02 $- $ L = 1 $- $ E(t) = 10 \sin 5t $---This will be shown on the educational website to help students understand how to apply Laplace transforms to differential equations and solve electrical circuit problems using differential equations.

According to our guidelines, we can answer only one question and the rest can be reposted.

Answered: Question #4 ( chapter La Place…

Question #4 ( chapter La Place Transform, online) Solve Y"+ Y = Sin(2t) using La place and inverse la Place transform Transform.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: f (t) ) — е -4(t-2)² e

Q: Not sure how to answer this problem

Q: Find the linear transform which converts the circle that has a radius 2 and center is (0,-2) to…

Q: What is harmonic, or Fourier analysis

A: Definition of harmonics "The term harmonic comes from acoustics. It refers to the vibration of a…

Q: Find the inverse transform of the equation below. R(s) = (S+7) / (s^2-3s-10)

A: We have to find inverse transform of R(s). Firstly by partial fraction simplify the fraction, Then…

Q: (s) = (1-3s) / (s^2+8s+21) A [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(-4t)] + [3*cos(sqrt(5)t)*e^ B…

Q: 36 3€ Find the laploce transform of f'(E) = e^†cos (6t) - e cos (Gt)

A: To find the laplace transform of ft=e3t+cos6t-e3t cos6t.

Q: use two and three points of Gaussian-Quadrature method to Find 1 = e" e(1+sinx) dx

Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

Q: In(√3) e dx 1+e²x A) tan-¹(3)-tan-¹(e) C) tan-¹(√3) E)-tan-¹(e)

A: Given integral: I=∫1ln3exdx1+e2x Let, u=ex Then, dudx=ex So, exdx=du Now, the lower limit becomes:…

Q: Dear tutor, please help me in inverse laplace transformation using only this table- formula below,…

A: e) Given to find L-15s-42s2-3 Formulas using here L-1ss2-w2=coshwtL-1ws2-w2=sinhwt

Q: Question 3 4. a) Integrate tan (0) sec (0)d0.

Q: (a) Determine the Fourier transform, g(m), of the signal in figure 1. Sketch g(m). f(t) 2 -1 1…

Q: If interest in a bank account is compounded continuously, the amount grows at a rate that is…

A: Solution: Given data, Initial amount P = $1000 rate r= 5% = 0.05 According to continuously…

Q: Find out a real-life problem, which can be solved using the Fourier Transform Techniques. Also, give…

A: A Fourier series is a way of representing a periodic function as a (possibly infinite) sum of sine…

Q: Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: sin(π ) ,…

Q: Q1: Solve using Laplace transform y + 4y = 8(t). y(0) = y'(0) = 0

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (+*+ ² + 2) = (0)4 -

A: Inverse Laplace transform of a function Fs is a piecewise continuous function ft with the following…

Q: Find sun alpha and tan alpha if the terminal side of alpha lies along the line y=-8x in Q2

Q: Results for this submission Entered 1/6ult-8)(e^(41-32)-e^(-2t+16)) The answer above is NOT correct.…

Q: Determine the Laplace Transform of cos*t

A: cos3t≡(cost)(cos2 t) cos3t=cos(1−sin2 t) cos3t=cost⋅1/2(1+cos2t)…

Q: Rectangle PQRS is reflected across the x-axis. The image is P'Q'R'S'.Which two further…

A: Given Rectangle PQRS is reflected across x axis then image is P'Q'R'S'

Q: 더 - C 1 -2s +6 s+2 82 - 4s + 8+1 C S-2 1

Q: S , use the translation property to compute eat cos bt). *** Given that cos bt)(s) = s². Click here…

A: The translation property is: Leatft=Fs-a

Q: We can now rewrite L{y} as follows. (금) . (공) Liy} S- 5 s+ 4 Next, to solve for y, we apply the…

Q: Integrate using Trigonometric Transformation cos 5 (In z)da a csc® (In æ)

Q: do the inverse laplace transforms of the rational function F(s)=(s-2)/s(s^2 -4s+8)

Q: Evaluate OI 4 sin ³x dx sin*x + C -sin¹x + C +cos³x + C -cost + +C cost --cos³x + C

Q: (a) sec¹ (31) √tan(3t) dt

Q: Since (7t^2) *e^(mt) - (7t^2) *sinh(at) = (t^2)(7e^(mt) - 7sinh(at)) What should you take the second…

Q: Find the inverse Laplace transform of L- s-37+4J- 3 (++3)²+4 3 3t e e 3t sin2t sin2t (s+3)2 (C) L"f…

A: Answer

Q: Let. a 3 = (-) = -(1) - P = ( ) 5 and a) Find Fourier Coefficient of b with respect to a . b) Find…

Q: I am not fully grasping the transformation from sinx to tanx and from cosx to tanx in step 2 of the…

A: To evaluate the following integral by using the substitution .Note: Since, the student has mentioned…

Q: Prove that the Dirac delta function satisfies +∞ 1 S(t – t') = 2/= t 2π ģ exp(-iw[t − t']) dw,

A: First recall the definition of Fourier transform and inverse Fourier transform of a function The…

Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric function properties

Q: Question 2: Calculate the inverse Laplace transform of the function F(s) = (s + 1)/(s^2 + 4s + 5).

Q: find 2d Fourier transform of e^(-4pi*(x^2+y^2)) the answer is e^(-pi(x^2+y^2)/2) why?

A: Find the 2d Fourier transform of the given function and the 2D transform of f is defined by the…

Q: Find the fourier serious of cos(2x)^2 on (-pi,pi)

A: We have to find the Fourier series expansion of f(x)=cos2(2x) on -π,π. The given function…

Question

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Laplace Transformation$

Learn more about

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

Similar questions

Activity 2 Differentiate the following. 1. y = sin(6x) 2. y = sin (5x – 2) 3. y = tan (2x3 + 5) 4. у %3D е2х- 3 5. y = e4x + 7
Question 1 Use the Bisection Method to estimate the root/s of the equation 2xCos(2x)-(x+1) = 0 stopping when f(*„)|< 5x10-3.
Question: Find Inverse Laplace Transform F(S)=2s- 3/(S^2-4) find inverse laplace transform f(s)=2s-3/(s^2-4)
Show Complete Solution
FIND LAPLACE TRANSFORM
Find the inverse transform of the equation below. V(s) = (1-3s) / (s^2+8s+21) [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(-4t)] - A [3*cos(sqrt(5)t)*e^(4t)] [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^{-4t)] - В [3*cos(sqrt(5)t)*e^{-4t)] [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(4t)] - [3*cos(sqrt(5)t)*e^{(4t)] [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(-4t)] + D [3*cos(sqrt(5)t)*e^(-4t)] [(13*sqrt(5)/5)*cos(sqrt(5)t)*e^(-4t)] - E [3*sin(sqrt(5)t)*e^(-4t)] [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(4t)] - F [3*cos(sqrt(5)t)*e^(-4t)]
#7,8 Please answer these 2 problems with clear and complete solutions.thank you
Solve for Fourier coefficient, Ssin x 02x27 f(x)= 0 T >x 22n cosx sec x + cosx csc csc² x csc? x secx cos? x cos x cos x § f(x)dx _ ? If f(x)* , then 1
Determine L^-1 {F}. F(s) = 8s³ - 8s² - 3s +6 / s^3 (S-2) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. £¯¹ {F} =
Find the inverse Laplace transform of the function F(s)=(s- 4)e^-3s/(s^3 + 4s)
Write a matlab program plotting a graph with the two equations below: a(y) = (y + pi)sin(y^2 + 0.5) z(y) = (sin(2piy)cos(2piy)/exp(y - 1)) - (5/2)
3) WHEN ANSWERING THE QUESTION PLEASE BE REALLY CLEAR ON EACH STEP AND USE TEXT(KEYBOARD NOT HANDWRITING) TO SHOW THE WORK IF POSSIBLE SINCE IS EASIER TO UNDERSTAND. AGAIN, BE CAREFUL ANSWERING, THANKS.