Question: The forced damped Duffing equation is given by x''+2x' + x + =fsinrtao Use the harmonic balance method to solve the equation of motion and

The forced damped Duffing equation is given by

x''+2ςx' + x +ε =fsinrtao

Use the harmonic balance method to solve the equation of motion and find the steady state solution. Then solve equation of motion numerically using MATLAB ODE solver ODE45, for initial conditions which are:

x'(0)=0, x(0)=0.85

ξ=0.38

f=0.34+(0.1:0.1:0.5)

r=(0.4:0.4:2.2)

Show the full working out including the MATLAB code.

Step by Step Solution

★★★★★

3.40 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Answer The MAtlab code Parameters xi 038 Damping ratio epsilon 01 Forcing amplitude frequencies 034 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mechanical Engineering Questions!

The two-dimensional wave equation is given by By letting ?jm,n denote the finite difference approximation of ?(xm, zn, tj), show that the finite difference scheme for the wave equation is Where h =...

A parametric equation is given by x = sin(t)cos(t), y = 1 .5cos(t) Plot the function for

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, give the solution with y arbitrary. For systems in three variables with...

The trial balance for LPO at 31 December 2013 was as follows: Notes: (i) Closing inventory at 31 December 2013 was $562,000. (ii) On 31 December 2013, LPO disposed of some obsolete plant and...

(a) LEP Table 12-2: Exothermic Reaction with Heat Exchange Download the Polymath, MATLAB, Python, or Wolfram codes for the algorithm and data given in Table T12-2 for the exothermic gas phase...

In Problems 36 through 38, apply the convolution theorem to derive the indicated solution x(t) of the given differential equation with initial conditions x(0) = x'(0) = 0. x" + 4x = f(t); x (t) = >=...

A dog sees a rabbit running in a straight line across an open field and gives chase. In a rectangular coordinate system (as shown in the figure), assume: (i) The rabbit is at the origin and the dog...

Given the formula (x) = x2 + 8x 12 (a) Determine the maximum and the corresponding value of x for this function analytically (i.e., using differentiation). (b) Verify that Eq. (13.7) yields the same...

The differential equation for the velocity of a bungee of a jumper is different depending on whether the jumper has fallen to a distance where the cord is fully extended and begins to stretch. Thus,...

In each of Problems 23-30, a second-order differential equation and its general solution y(x) are given. Determine the constants A and B so as to find a solution of the differential equation that...

Does the fact that public decisions are sometimes made by self-interested politicians and bureaucrats undermine the efficiency of public-sector decision making?

Find the area of the region between the curves y = |x| and y=x-2.

12. Which of the following assigns the string Rover to the fifth element in a one-dimensional array named strPetNames? a. strPetNames(4) = "Rover" b. strPetNames[4] = "Rover" c. strPetNames(5) =...

A race car moves such that its position fits the relationship: x = (5.0 m/s)t + (0.75 m/s3)t3 where x is measured in meters and t in seconds. (a) Plot a graph of the cars position versus time. (b)...

Write a program that will convert degrees celsius to degrees fahrenheit.

Write a program that will convert degrees fahrenheit to degrees celsius.

the beam shown in the figure, if w=20 KNm and P-30 KN, swer the following questions 6) The shear force [KN] # point Cin KNJ a) 42.8 17) The bending moment at point Cin KNm) b) 36.7 c) 41.7 d) 27.2 e)...

To open a combination lock, you turn the dial to the right and stop at a number; then you turn it to the left and stop at a second number. Finally, you turn the dial back to the right and stop at a...

A previously healthy 33-year-old woman presents with dyspnea on exertion and cough. Chest radiograph shows bilateral hilar adenopathy and mild diffuse parenchymal infiltrates. A diagnosis of...

- Consider an underdamped undriven oscillator with a period of 1 s, starting from 80 = 0.1 and wo = 0. Sketch qualitatively correct vs t, and w vs t plots for several periods and an w vs plot...

Oscillations Goal: The goal of this mini-project is to design a suspension system for a car. There are two essential components for such a system: springs and shock absorbers. Youre going to write a...

Here is my code in C for plotting the amplitude versus w/w0 for the Duffing equation : #include #include #include // Duffing Equation double f(double t, double x, double y, double gamma, double w0,...

Here is my code to plot in c the amplitude versus w/w0 for the Duffing equation without the x^3 dependecy : #include #include #include double f(double t, double x, double y, double gamma, double w0,...

(0) Here is my code in C for plotting the amplitude versus w/w0 for the Duffing equation : #include #include #include // Duffing Equation double f(double t, double x, double y, double gamma, double...

A forced damped oscillator is govern by the equation: C K Fo + cos wt m m m k where wo = m The particular solution of the non homogeneous second order equation is given by: Xp (t) = A cos wt + B sin...