Question: Suppose the illustrated planar structure has unit masses at the nodes and the bars are all of unit stiffness. (a) Write down the system of

Suppose the illustrated planar structure has unit masses at the nodes and the bars are all of unit stiffness.

(a) Write down the system of differential equations that describes the dynamical vibrations of the structure.
(b) How many independent modes of vibration are there?
(c) Find numerical values for the vibrational frequencies.
(d) Describe what happens when the structure vibrates in each of the normal modes.
(e) Suppose the left-hand mass is displaced a unit horizontal distance. Determine the subsequent motion.

Step by Step Solution

★★★★★

3.34 Rating (178 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a are the horizontal and vertical displacements of the two free nodes b 4 c 1 1 12 2 541196 2 2 12 2 ... 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 (1 attachment)

952-M-L-A-E (2841).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

All the bars in the illustrated square planar structure have unit stiffness. (a) Write down the reduced incidence matrix A. (b) Write down the equilibrium equations for the structure when subjected...

Assuming unit masses at the nodes, find the vibra-tional frequencies and describe the normal modes for the following planar structures. What initial conditions will not excite its instabilities...

(a) Suppose that we fix one node in a planar structure and put a second node on a roller. Does the structure admit any rigid motions? (b) How many rollers are needed to prevent all rigid motions in a...

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

Can you please help me with number 12 and number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.6 Problems Find...

Can you please help me with number 12 and number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.7 Matrix Exponentials...

subject: Differential Equations pls read instructions do not use ai. drop all references and link Instructions ODE application. - find an article related to ODE application - provide a short...

Can you please help me with number 21. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! Open with Chapter 5 Linear Systems...

Can you please help me with number 31. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.7 Matrix Exponentials and Linear...

Can you please help me with number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! Linear Systems quations 406 The...

Change from rectangular to cylindrical coordinates. (Let r 0 and 0 2 ) (a) (-9, 9, 9) (b) (-5, 53, 3)

Mr. Smith wishes to retire in ten years time. He requires a pension of $8 000 per month for twenty years, commencing the month immediately after the month he retires. A nominal (quoted) interest rate...

Which one of the following takes up the greatest percentage of the benefits dollar spe A Legally required contributions such as social security, unemployment, a Paid rest periods such as coffee...

According to an economic research paper, the existence of a large public debt may hinder capital accumulation, crowding out private investment; therefore, it reduces economic growth rates. In this...

Sketch the graph of an example of a function f that satisfies all of the given conditions. 5. f(0) = 0. f(1) = 1. lim f(x) = 0. f is odd 6. lim f(x) = 00, lim f(r) = -. lim f(x) 1 lim f(x) = 1. %3D...

Guess the value of the limit by evaluating the function f(x) = x2/2x for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 50, and 100. Then use a graph of to support your guess lim 2'

(a) Use a graph of to estimate the value of lim x→∞ f(x) correct to two decimal places. (b) Use a table of values of f(x) to estimate the limit to four decimal places. f(x) = -)-

A loan with the following terms is being made: Fixed rate, constant monthly payment. Closing date February 9th. Five percent interest rate. Prepaid interest due at closing. $120,000 mortgage loan...

(20 points) Your company is considering a five-year project to boost your sales. By purchasing a new machine, you expect to increase sales by X units in years 1 through 5. The per unit price is $70,...

In ZIMS store the manager is interested in determining which items sell well together. The manager assigned you this task and you opted for using Apriori Algorithm for finding the frequent item sets...