In this assignment, you will be asked to watch a short video and perform some applications that have to do with solving second order differential equations with constant coefficients. These differential equations can be solved using the method of annihilators. There are two primary applications that we will be studying:
1. Spring Mass Systems 2. RLC Circuits
You can take any notes that you feel are necessary for you to understand the applications and solve for their models. What we are primarily looking for is the function that will model the particular situation based upon the differential equation. And then we will be discussing how we can use the D.E. and the model to ascertain key characteristics of the modeled situation.
Spring Mass Systems:
1. Basic setup of the spring mass system. Construct a diagram of the basic spring mass system setup and construct the differential equation. Make sure that you include what the variables in the differential equation mean.
2. Consider the following initial-value problem for the spring mass system.
??2?? ????2
+ 2 ???? ????
+ ?? = 0, ??(0) = −1, ???? ????
(0) = 2
a. Is the system overdamped, underdamped or critically damped? Explain how you know. b. Determine if the system passes through the equilibrium position. If it does, give the
time t.
3. Suppose that you have a spring mass system. The mass on the system is 1 g. The spring mass constant is 25. In this situation there is no damping, but there is an external force acting on the system that is modeled by the function, ??(??) = 75 cos 5??. Construct the differential equation for the spring mass system and then solve for ??(??).
a. In this situation, is there resonance? Explain how you know. b. Suppose that you let the spring mass continue to oscillate for a very long time, give a
function that models the movement after this very long time t (e.g. find the steady state of the system).
RLC Circuits 1. Construct a diagram of the basic RLC Circuit and construct the differential equation. Make sure
that you include what the variables in the differential equation mean. 2. Suppose that you have a circuit with a resistance of 2 Ω, inductance of 2
11 H and a capacitance of
11 60
F. An EMF with equation of ??(??) = 6 cos 4?? supplies a continuous charge to the circuit. Suppose that the q(0)= 8 V and the q’(0)=7.
3. Determine the steady state solution and transient part of the circuits current.
Why Work with Us
Top Quality and Well-Researched Papers
Our writers have been trained on how to handle papers placed by our clients. The writer must read and understand before embarking on writing the papers. In case of any issue that needs clarification, writers are encouraged to ask the client or support.
Professional and Experienced Academic Writers
Our team comprises of the best writers and editors. We do thorough vetting during recruitment to make sure that our writers have the knowledge and experience we aspire in the team.
Free Unlimited Revisions
Our aim is to give the client the best outcome. If for some reason you are not satisfied with the wok done, you can ask the paper to be revised or rewritten. This will be done to your satisfaction with no extra charges.
Prompt Delivery and 100% Money-Back-Guarantee
We have writers who work round the clock. This helps in making sure that all our clients’ papers are delivered on time. If we have issues with the deadline, we will ask for extension. If its not possible, the money is fully refunded.
Original & Confidential
Our clients’ confidentiality is highly respected. We can never disclose our clients’ details to third parties. In the same regard, we strive to give our clients 100% original papers. We do not tolerate plagiarism from our writers.
24/7 Customer Support
Clients can reach us any time of the day, and any day of the week. There is a live chat, email or phone numbers to help in ease of communication.
Try it now!
How it works?
Follow these simple steps to get your paper done
Place your order
Fill in the order form and provide all details of your assignment.
Proceed with the payment
Choose the payment system that suits you most.
Receive the final file
Once your paper is ready, we will email it to you.
Our Services
You should never be worried about your papers even in the middle of the night. Our team will work round the clock to deliver.
Essays
We have an able team that can deliver your work in the shortest time possible. The academic level or the type of work should never be a hindrance. Our highly competent support team is always around (24/7) to give you any assistance you may need.
Admissions
Admission Essays & Business Writing Help
Do you need to be admitted in your dream institution but find it challenging to write an admission essay? Our team is in a position to write the best letter that will guarantee you an admission. We do as well write the best business proposals and reports.
Reviews
Editing Support
Writing can be fun and enjoyable when everything has been done right. Writing is not just enough without proper editing and proofreading. We have a team of editors that ensure everything falls in place, whether its issues to do with grammar or referencing styles.
Reviews
Revision Support
Once the paper has been done and submitted, that is not the end of it. You can always ask for amendment or improvement if you feel something has not been done right. Our team of writers and editors will gladly assist you to your satisfaction. Revision is free of charge.