# Mechanical math

Question 1
Consider the mechanical system with three degrees of freedom shown below. The positions of the particles are measured from their equilibrium positions. The system has a normal mode eigenvector (6.57, b, 6.57)T.
Â  If all particles start from their equilibrium positionsÂ and the leftmost and rightmost particles are given a velocity of 34.22 ms-1,Â the velocity of the middle particle is -47 ms-1,Â the system willÂ oscillate in a normal mode. Determine the value of b, giving your answer to 3 decimal places.

Document Preview:

Question 1
Consider the mechanical system with three degrees of freedom shown below. The positions of the particles are measured from their equilibrium positions. The system has a normal mode eigenvector (6.57, b, 6.57)T.
Â  If all particles start from their equilibrium positionsÂ and the leftmost and rightmost particles are given a velocity of 34.22 ms-1,Â the velocity of the middle particle is -47 ms-1,Â the system willÂ oscillate in a normal mode. Determine the value of b, giving your answer to 3 decimal places.
Question 2
An external sinusoidal force is applied to an oscillating system which can be modelled by a model spring and a damper. The general solution of the equation of the motion is given by,
x = 3Â + 3.183cos(2t â€“ ) + 3.18exp(-7.72t)Â cos(t + )
where , , and Â are some constants . DetermineÂ the amplitude of the oscillation when steady-stateÂ is reached. Give your answer correct toÂ 3 decimal places.
Question 3
Consider two particles of masses m1 and m2 joined to each other and to two fixed walls at both ends by three identical model springs of stiffness k and natural length lo. The matrix equation of motion for the mechanical system is shown below . For certain choices of m1, m2 and k, a normal mode of the system is given byÂ (x1(t), x2(t))T where a, b, ? andÂ Â are some constants. If a = -3.77, b = 15, determine how far (in cm) to the left of its equilibrium position does m1 have be initially displaced if m2 is initially 4.09 cm to theÂ right of its equilibrium position, in order for the system to oscillate as a normal mode. Give your answer correct to 3 decimal places.
Question 4
A particle A of mass 2.22 kg collides with another particle B of mass 1.3 kg. Their initial velocities are u1 = 1.55i + 0.88j and u2 = 0.21i + 0.94j just beforeÂ impact. After collision, they both merged and becomes a composite particle, which travel with a velocity of V =Â 0.67 i + 0.99j. Calculate the change in kinetic energy. Give yourâ€¦

Attachments:

# Our Service Charter

1. ### Excellent Quality / 100% Plagiarism-Free

We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers.
2. ### Free Revisions

We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed.
3. ### Confidentiality / 100% No Disclosure

We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service.
4. ### Money Back Guarantee

If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit.

We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.

Excellent Quality
Zero Plagiarism
Expert Writers

or