Question: The nonlinear mass-spring system is described by the second order differential equation: mx + k(x + x) = 0, where m, k and are

The nonlinear mass-spring system is described by the second order differential equation: mx + k(x + x) = 0, where m, k and are constants and the displacement x is a function of time t. 4.1. (5 marks) Work out and state the algorithmic equations for applying the symplectic Euler method to solve equation (2). 4.2. (5 marks) Show how your MATLAB function from Task 1 can be adapted to account for the additional parameter B. (2) 4.3. (20 marks) Write a MATLAB program to create a plot comparing the displacement versus time calculated by (a) the symplectic Euler method with 200 time steps and (b) MATLAB's ode45. Use the parameter values given on page 1. Include the plot in your report and describe your observations.

Step by Step Solution

★★★★★

3.40 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

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 Chemistry Questions!

Over an integer array A[0...n-1] of size n, answer the following questions. (a) What is the complexity of searching for a key k over A? Assume that ke A, and answer for the average case. (b) What is...

Write a program to (1) plot the graphs of the ideal body weights (IBM) for males and females for the heights ranging from 50 inches to 78 inches, and (2) asking the users to enter their sex, weight,...

Use the Chapman model to explore the behaviour of a model atmosphere consisting of pure 0, at 10 Torr and 298 K that is exposed to measurable frequencies and intensities of UV radiation. (a) Look up...

The following data were taken from the year- end records of Glare Import Company: Required: Fill in all of the missing amounts. Show computations. Year 2 Statement of Eamings Items Gross sales venue...

The level of inventory of a manufactured product has increased by 8,000 units during a period. The following data are also available: Unit manufacturing costs of the period: Variable: $24 Fixed: $10...

=+2. Assume that the equipment was depreciated under the double-declining-balance method. In the first week of the fifth year, the equipment was sold for $10,000. Journalize the entry to record the...

Review the same test and determine to what extent you think it is appropriate for males and females, people of different racial and ethnic backgrounds, people whose primary language is not English,...

What is Kellys basis for her partnership interest in each of the following independent situations? The partners share the economic risk of loss from recourse liabilities according to their...

Financial Statements Describe a transaction that would: Decrease both a liability and an asset. Increase both an asset and retained earnings. Decrease both an asset and retained earnings. Increase...

The bar codes above represent locations in a warehouse. How many units would be left in each location? If you picked 250 units from location 00000113774360000 If you picked 250 units from location 00...

5. (20 points) The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in dollars) from each plant...

] Scenario and Instructions Imagine that you just began working in the position and at the sport organization of your dreams. A good friend who worked there in the past has told you that although the...

Part A - Calculate a Reynolds number A jet of length L = 17.5 m is travelling at V = 410 m/s at an altitude of h = 7 km. At that altitude, the speed of sound is c = 312 m/s, the density of air is p =...

Choose any business of your choice and mention the Cost- benefit analysis briefly to conduct that business.

Calculate the earnings after tax and dividends under each of the following two financing options based on the document: stock financing: $20 million with 8 percent annual dividend.

Assume that the clamp shown has been tightened on wooden planks being glued together until P = 300 N. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to...

is gamification an ethical motivation practice for employers to use?

For each of the following transactions, indicate whether it increases, decreases, or has no effect on the following financial ratios: current ratio, debt-to-equity ratio, profit margin ratio, and...

Solve the following initial-value problem from t = 4 to 5: dy/dt = 2y/t Use a step size of 0.5 and initial values of y(2.5) = 0.48, y(3) = 0.333333, y(3.5) = 0.244898, and y(4) = 0.1875. Obtain your...

Perform the same computation as in Sec. 8.3, but determine the value of C required for the circuit to dissipate to 1% of its original value in t = 0.05 s, given R = 280 , and L = 7.5 H. Use (a) A...

A manufacturer provides specialized microchips. During the next 3 months its sales, costs, and available time are There are no chips in stock at the beginning of the first month. It takes 1.5 hrs of...

T F When people start losing significant amounts of weight, their bodies respond as though they were starving. (p. 347)

9.7 Evaluate methods used to treat sleep-wake disorders.

8.7 Explain how cocaine affects the brain.