Question: Consider a mass-spring system with damping. Suppose the object has unit mass, the coefficient of friction is b = 1 and the spring constant is

Consider a mass-spring system with damping. Suppose the object has unit mass, the coefficient of friction is b = 1 and the spring constant is k = 1/2. The differential equation describing this situation is

i. Convert the 2 ^nd order DE into a first-order system in the variables y and v. plot its direction field using Bluffton and consider why solutions behave as they do in terms of the spring and damping constants.

ii. Solve the system and find the specific solution to it starting at y (0) = 1, v (0) = 2. Note y (t) is a solution to the 2 ^nd order DE.

iii. For your solution above, as t ? ? ?, what values do y (t) and v (t) approach?

dy dt + dy 1. +=y=0 dt

Step by Step Solution

★★★★★

3.37 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To solve this problem follow these steps i Convert the 2nd Order DE into a FirstOrder System Given t... 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

Document Format (2 attachments)

608f9db2a9a7e_21173.pdf

180 KBs PDF File

608f9db2a9a7e_21173.docx

120 KBs Word File

Students Have Also Explored These Related Mathematics Questions!

vb1-3) The proper period of a mass spring system with a massless spring is 0.285s, with the mass hanging on the spring and the spring itself hanging on the ceiling. 0.7s after the start of the...

Find a first order system of ordinary differential equations that has the indicated vector-valued function as a solution: (a) (b) (c) (d) (e) (f) (g) (h) 2 e ecos 3r 3e-sin 3r sin 2r cos 2 sin 21 3...

A direction field for the differential equation y = x sin y is shown. (a) Sketch the graphs of the solutions that satisfy the given initial conditions. (i) y (0) = 1 (ii) y (0) = 2 (iii) y (0) = π...

Write down the change equation for this system. Indicate what each term represents and include the units for each term. Exercise C. Consider the mass-spring systeln described on pp. 32-34 in the...

\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline & \multicolumn{8}{|c|}{ LIST OF AVAILABLE SPRINGS (helical compression springs) } & \\ \hline OD(in) & ID(in) & Length(in) & MaxLoad(lb) & MaxDeflection(in)...

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

1 Distributed Systems In a distributed electronic conference application each participant has a replica of a shared whiteboard. Only one user at a time may write to the whiteboard, after which the...

1 A mathematical model for the forces on a car suspension system The goal of this project is to describe one of the ways in which resonance phenomena. appear in the "real world\" and to use second...

Prolog You are approached to compose a Prolog program to work with twofold trees. Your code shouldn't depend on any library predicates and you ought to expect that the mediator is running without...

A creative engineer suggests structuring the TLB so that not all the bits of the presented address need match to result in a hit. Suggest how this might be achieved, and what might be the costs and...

Sam is interested in two goods, X and His indirect utility function is U* = Mpx -0.9 py (same as U* = M /(px0.9 py1-0.9)) 0.9-1. where M is Sam's income, and px and py denote respectively the price...

Suppose that country I and trading partner country II decrease their willingness to trade at the same time. What will be the impact on the terms of trade and on the volume of trade?

Fashion First 3 1 1 North Side Plaza Northwestern, WA 9 8 5 0 1 August 1 1 , 2 0 1 2 Sarah Levy 6 4 3 Glenwood Avenue Weston, CA 9 5 8 0 0 Dear Ms . Sarah Levy: ( 1 ) As a preferred customer and...

The following errors took place in journalizing and posting transactions: a. Insurance of $18,000 paid for the current year was recorded as a debit to Insurance Expense and a credit to Prepaid...

The unadjusted trial balance of Arlington Air Purification System at December 31, 2014, and the data needed for the adjustments follow. Adjustment data at December 31 follow: a. On December 15,...

The following preliminary unadjusted trial balance of Ranger Co., a sports ticket agency, does not balance: When the ledger and other records are reviewed, you discover the following: (1) the debits...

Summary information from the financial statements of two companies competing in the same industry follows. Required 1. For both companies compute the (a) Current ratio, (b) Acid-test ratio, (c)...

The accounts in the ledger of Hickory Furniture Company as of December 31, 2019, are listed in alphabetical order as follows. All accounts have normal balances. The balance of the cash account has...

12 Sites to Buy Verified Celsius Network Accounts with Established History Are you ready to dive into the world of cryptocurrency with confidence? The Celsius Network is making waves as a leading...

Consider a mass- spring system with damping. Suppose the object has unit mass, the coefficient of friction is b = 1 and the spring constant is k = 1/2. The differential equation describing this...

Consider the force balance for a damped harmonic oscillator with mass m = 1 kg, a spring constant k > 0 in N/m, and a friction coefficient > 0 in kg/s, subject to some initial position x 0 and...

watch the three short clips below then answer the questions Copy and paste the three links below 1) Projectile Motion https://www.nsf.govews/mmg/mmg_disp.jsp?med_id=72205&from= 2) Newton's Second Law...

The following differential equation models the position () of an object that is attached to a spring with respect to time (). The mass-spring system operates under the influence of both damping and...

Do it in MATLAB, Thanks function x = frsp_sdof(t) % Free response function of a SDOF system global m c k global x0 v0 wn = sqrt(k/m); % natural frequency ("omega_n") zeta = c/2/sqrt(k*m); % damping...

computer Science Question 1 : Heat Exchanger Design Part A: Calculate the heat transfer rate required for a heat exchanger to cool 1 5 0 0 kg / hr of water from 8 5 \ deg C to 3 0 \ deg C . Assume...