Suppose that when subject to a nonzero external force f 0, a massspring chain has equilibrium

Question:

Suppose that when subject to a nonzero external force f ≠ 0, a mass–spring chain has equilibrium position u^⋆. Prove that the potential energy is strictly negative at equilibrium: p(u^⋆) < 0.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

See More Books

Question Posted: Apr 21, 2023 09:16 AM

See More Questions

A spring with Mass the preceding problems in this chapter have assumed that the springs had negligible mass. But of course no spring is completely mass less. To find the effect of the spring's mass,...
19 g of molten SnCl is electrolysed for some time using inert electrodes until 0.119 g of Sn is deposited at the cathode. No substance is lost during electrolysis. Find the ratio of the masses of...
Evaluate and simplify the following derivatives. d dx -(x Inx)
A thirty-year U.S. Treasury bond has a 4.0 percent interest rate. In contrast, a ten-year Treasury bond has an interest rate of 3.7 percent. If inflation is expected to average 1.5 percentage points...
Susan's mother is currently living in a nursing home, and she is worried about the financial drain of her mother's long-term care costs. She would like to start planning for her own potential future...
A tank of oxygen has a hole of area $0.5 \mathrm{~cm}^{2}$ in its wall. The temperature of the oxygen in the tank is $25^{\circ} \mathrm{C}$. Calculate the rate $(\mathrm{kg} / \mathrm{s})$ at...
Barbara Whitley had great expectations about her future as she sat at her graduation ceremony in May 2015. She was about to receive her Master of Accountancy degree, and the following week she would...
Discuss the significance of sustainable agriculture practices in achieving food security and environmental sustainability, focusing on techniques such as organic farming, agroecology, precision...
Without doing any calculations, indicate whether the suggested change in the allocation of fixed manufacturing costs would increase, decrease, or leave unchanged next year's estimated pre-tax income....
What is the analogue of condition (6.33) for a disconnected graph? z. f = f + f + ... + fn = 0,
Suppose all bars have unit stiffness. Explain why the internal forces in a structure form the solution of minimal Euclidean norm among all solutions to AT y = f.
Stevens Restorations was organized in January 2011. During 2011, Stevens engaged in the following stockholders equity activities: a. Secured approval for a corporate charter that authorizes Stevens...
Given f(x)=7x - 3 a) Evaluate f(-2) f(-2)=-17 b) Solve f(x) = 18 T
(a) An oil producer enters into a one-year short forward contract to sell 6000 barrels of oil for $74 per barrel when the spot (market) price is $72 per barrel. The spot (market) price in one year...
Solve logx-log26-log25+ 2log23 for x.
From the results of the 2000 census, the population in Sukarame Village was 4,735 people, consisting of 1,941 people aged 0 - 14 years, 2,431 people aged 15 - 64 years and the rest over 64 years old....
1 Given log 3 what is log, 9? 4'
The full-time equivalent enrollment (FTE enrollment) at a college is the number of full time students it would take for their total credits (units or hours) to equal the total credits in which both...
What is the difference between the straight-line method of depreciation and the written down value method? Which method is more appropriate for reporting earnings?
Which of the following are vector spaces? Justify your answer! (a) The set of all row vectors of the form (a, 3a). (b) The set of all vectors of the form (a, a + 1). (c) The set of all continuous...
Let V = Cn(R) be the vector space consisting of all continuous functions f: R R. Explain why the set of all functions such that f(1) = 0 forms a subspace, but the set of functions such that f(0) = 1...
Let V = C ([a, b|) be the vector space consisting of all functions f(t) which are defined and continuous on the interval 0 ¤ t ¤ 1. Which of the following conditions define subspaces of...
Background embezzlement investigate and share one or two cases that were in the media here in the US several years ago and even movies and documentaries have been made of one of these "individuals."
Ratio of liabilities to stockholders' equity The following data were taken from Alvarado Company's balance sheet: Dec. 31, 20Y4 Dec. 31, 20Y3 Total liabilities Total stockholders' equity $4,085,000...
January 4 , 2 0 x 2 , you conducted a surprise count in connection with your audit of the financial statements of Theo Corp. for the year ended December 3 1 , 2 0 x 1 . The following were identified...

Suppose that when subject to a nonzero external force f 0, a massspring chain has equilibrium

Question:

Step by Step Answer:

ANSWER Let the massspring chain be described by the equation m u k u f where u is the displacement o...View the full answer

Applied Linear Algebra

Students also viewed these Mathematics questions