25.18 The following is an initial-value, second-order differential equation:d²x + (5x) dx + (x + 7) sin (wt) = 0dt²dtwheredx (0)(0) = 1.5 and x(0) = 6dtNote that w= 1. Decompose the equation into two first-order differential equations. After thedecomposition, solve the system from t = 0 to 15 and plot the results of x versus time and dx/dt versus time.

To decompose the given second-order differential equation into a system of first-order differential…

Answered: 25.18 The following is an…

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.6P

See similar textbooks

Similar questions

Q(s) = S5 + 2S4 + 2S3 + 4S2 + 11S + 10 = 0 i). Identify the stability of the system using Routh Hurwitz Algorithm. (ii). Comment about the Roots location.
Response using Laplace transformation.
Derive the governing differential equation for each system with the chosen generalized coordinate. SEE THE IMAGE BELOW Answers: 1. GDE: (5/2) mẍ + (5/4) kx = 0 2. GDE: (7/48) mL² ϴ [note: theta symbol has two dots above) + (3/8) cL² ϴ [ note: theta symbol has one dot above] + 5 kL² ϴ = 0
1) Second order stress tensor represents the state of stress at a point in a mechanical part (SEE IMAGES). The eigenvalues of σ are the principal stresses at the corresponding point, which are important for determining when the mechanical part will yield. Use the characteristic equation to determine the principal stresses of σ. Please show your steps. 2) Given that an eigenvector, v, corresponding to a particular eigenvalue, λ˜, of σ must satisfy (σ − λ˜I)v = 0, find the eigenvectors associated with the eigenvalues from (b). You may use software to verify your answer but please show your steps. Draw the eigenvector and eigenvalue.
laplace transform
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
In this exercise we show that in the general case, exact recovery of a linear compression scheme is impossible. a. Let A ∈ Rn,d be anarbitrary compression matrix where n ≤ d−1. Show that there exists u,v ∈ Rd,u= v, such that Au = Av. Hint: Show that there exists u= 0,v = 0 such that Au = Av = 0. Hint: Consider using the rank-nullity theorem. b. Conclude that exact recovery of a linear compression scheme is impossible.
Suppose a spring with spring constant k=1 supports a mass of 1kg and is subject to a driving force f(t)=sin2t. The mass is initially at rest at its equilibrium point. At time t=2, the mass is hit with a sharp upward blow, so that the force of the blow is δ(t−2). Set up and solve (using Laplace transforms) an initial-value problem modelling this situation.
Response using matlab.
Can you solve this without the transformation matrix and if thtas not possible explain what they do. Also can you explain why you need to change from the J2000 state to geocentric equatorial frame. also would this code work to solve the problem?: % Step 1: Define the initial state vector at burnout r0 = [5210.345121, -549.481941, 4300.883291]; % Position vector [km] v0 = [-1.451280 7.391098 2.690198]; % Velocity vector [km/s] % Step 2: Calculate the initial velocity magnitude and specific angular momentum v0_mag = norm(v0); % Initial velocity magnitude [km/s] h0 = cross(r0, v0); % Specific angular momentum vector [km^2/s] h0_mag =…
For the DE: dy/dx=2x-y y(0)=2 with h=0.2, solve for y using each method below in the range of 0 <= x <= 3: Q1) Using Matlab to employ the Euler Method (Sect 2.4) Q2) Using Matlab to employ the Improved Euler Method (Sect 2.5 close all clear all % Let's program exact soln for i=1:5 x_exact(i)=0.5*i-0.5; y_exact(i)=-x_exact(i)-1+exp(x_exact(i)); end plot(x_exact,y_exact,'b') % now for Euler's h=0.5 x_EM(1)=0; y_EM(1)=0; for i=2:5 x_EM(i)=x_EM(i-1)+h; y_EM(i)=y_EM(i-1)+(h*(x_EM(i-1)+y_EM(i-1))); end hold on plot (x_EM,y_EM,'r') % Improved Euler's Method h=0.5 x_IE(1)=0; y_IE(1)=0; for i=2:1:5 kA=x_IE(i-1)+y_IE(i-1); u=y_IE(i-1)+h*kA; x_IE(i)=x_IE(i-1)+h; kB=x_IE(i)+u; k=(kA+kB)/2; y_IE(i)=y_IE(i-1)+h*k; end hold on plot(x_IE,y_IE,'k')

SEE MORE QUESTIONS

Recommended textbooks for you

Principles of Heat Transfer (Activate Learning wi…

Mechanical Engineering

ISBN:

9781305387102

Author:

Kreith, Frank; Manglik, Raj M.

Publisher:

Cengage Learning