Home / Questions / Two masses and three springs Two identical masses M are hung between three identical spri...
Two masses and three springs*
Two identical masses M are hung between three identical springs. Each spring is massless and has spring constant k . The masses are connected as shown to a dashpot of negligible mass. Neglect gravity.
The dashpot exerts a force bv , where v is the relative velocity of its two ends. The force opposes the motion. Let x _{1 }and x _{2 }be the displacements of the two masses from equilibrium.
Find the equation of motion for each mass.
Show that the equations of motion can be solved in terms of the new dependent variables y _{1 }= x _{1 }+ x _{2 }and y _{2 }= x _{1 }− x _{2 }.
Show that if the masses are initially at rest and mass 1 is given an initial velocity v _{0 }, the motion of the masses after a suﬃ-
ciently long time is
Evaluate ω .
x _{1 }= x _{2}
_{= }v _{0}
2 ω
Jun 19 2020 View more View Less
What is the name of the Account Titles of : Accrued interest of $150 that has not yet been paid.
Sep 02 2020On average, one preganglionic neuron synapses with eight or nine postganglionic neurons, each innervating a different target.33) It is important during stress or emergenc...
Dec 19 2019If Tellco's common stock dividends are projected to be $1.21 next year, and the shares are currently trading at $32.50, what is the cost of retained earnings, given growt...
Aug 14 2021A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of 3.0 4.1 cm in contact with the floor. The total mass of the s...
Aug 21 2021Assume a firm is financed with 30% debt on which it pays 9%. What is the expected return on equity if the expected return on assets is 14%?A. 16.14%B. 17.86%C. 14.92%D. 15.50%
Jun 08 2021Which of the following illustrates the law of supply?A. An increase in the number of firms in the industry causes a shift of the supply curveB. An increase in price cause...
Apr 26 2021Introduction to tax acct 321.Wnedy sold office furniture for $120,000. The initial cost was $100,000 and she has taken $50,000 of depreciation. How much section 1231 gain...
Jul 22 2021Henry Hatfield, CPA, was hired to prepare audited financial statements for Happy Campers, a nonprofit organization providing summer camp scholarships for inner-city, low-...
Aug 15 2021A sample of ethylene glycol has a mass of . The sample absorbs of heat. The initial temperature of the sample is . What is the final temperature? The specific heat capac...
Aug 17 2021A cat drops from a shelf above the floor and lands on all four feet His legs bring him to a stop in a distance of
Feb 15 2020