Fig. Q1 shows an inverted pendulum consisting of a spherical ball of radius R and mass...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Fig. Q1 shows an inverted pendulum consisting of a spherical ball of radius R and mass m₂ and a uniform rod of mass my and length a. Pendulum is pivoted at O. Two springs, each of stiffness k, are attached to the ball as shown in the figure. Determine the equation of motion and derive an expression for the natural frequency of vibrations of the system. Take the moment of inertia of a sphere about its centre as mr², where m is the mass and r is the 5 radius of the sphere. m a If m₁ = m, m₂ = and R. show that the natural frequency oo, is approximately given 5 4 by 00=0.438 25 3 m a What is the condition for stability of the system? m₂! mi B anton Fig. Q1 m Fig. Q1 shows an inverted pendulum consisting of a spherical ball of radius R and mass m₂ and a uniform rod of mass my and length a. Pendulum is pivoted at O. Two springs, each of stiffness k, are attached to the ball as shown in the figure. Determine the equation of motion and derive an expression for the natural frequency of vibrations of the system. Take the moment of inertia of a sphere about its centre as mr², where m is the mass and r is the 5 radius of the sphere. m a If m₁ = m, m₂ = and R. show that the natural frequency oo, is approximately given 5 4 by 00=0.438 25 3 m a What is the condition for stability of the system? m₂! mi B anton Fig. Q1 m
Expert Answer:
Answer rating: 100% (QA)
To determine the equation of motion and the natural frequency of vibrations for the given system let... View the full answer
Related Book For
Fundamentals of Ethics for Scientists and Engineers
ISBN: 978-0195134889
1st Edition
Authors: Edmund G. Seebauer, Robert L. Barry
Posted Date:
Students also viewed these accounting questions
-
Find the points on the ellipse that are farthest away from the point (1, 0). (Round your answers to the nearest hundredth.) 4x + y = 4 ) (larger y-value) ) (smaller y-value) Need Help? Watch It...
-
A cylinder with radius R and mass M has density that increases linearly with distance r from the cylinder axis, p = ar, where a is a positive constant (a) Calculate the moment of inertia of the...
-
A smaller disk of radius r and mass m is attached rigidly to the face of a second larger disk of radius R and mass M as shown in Figure P15.69. The center of the small disk is located at the edge of...
-
The costs of achieving emission reductions in the future will depend greatly on the types of policies used to reduce emissions today. Explain.
-
Angela, who is single, incurs circulation expenditures of $153,000 during 2014. She is in the process of deciding whether to expense the $153,000 or to capitalize it and elect to deduct it over a...
-
a . When does the allowance method recognize the bad debt expense for a years sales? b . When a specific account receivable is written off using the allowance method, which accounts are debited and...
-
How you may use computers for litigation support?
-
Marie Hardys will has the following provisions: I leave the cash balance deposited in the First National Bank (up to a total of $50,000) to Jack Abrams. I leave $18,000 cash to Suzanne Benton. I...
-
The following cost-of-quality data were collected at the installment loan department of the Kenney Bank. Classify these data into the appropriate cost-of-quality categories. Quality Cost Loan...
-
Go back and quickly review the rules that the Sarbanes-Oxley Act of 2002 placed on the auditing profession as described in this chapter. What do you think are the two or three main purposes of these...
-
According to Buck et al there are specific changes that have redefined the modern marketing landscape. Which is NOT something that the founders of Headlands Distillery explicitly talk about? a.all...
-
How many lines does the following code output? A. One. B. Two. C. Three. D. Four. E. Five. F. None of the above. The code does not compile. public class Cars { static { } } private static void...
-
The following diagram shows two reference variables pointing to the same Bunny object in memory. The reference variable myBunny is of type Bunny, while unknownBunny is a valid but unknown data type....
-
The author of this method forgot to include the data type. Which of the following reference types can best fill in the blank to complete this method? A. String B. StringBuilder C. Both D. Neither...
-
Given the file Magnet.java shown, which of the marked lines can you independently insert the line var color; into and still have the code compile? // line al public class Magnet { // line a2 public...
-
Which of the following properties of an enum can be marked abstract? A. The enum type definition B. An enum method C. An enum value D. An enum constructor E. None of the above
-
GHI Corp. prepares it financial statements in accordance with U.S.GAAP. Its inventory valuation method is LIFO. Assume all purchases and sales are on credit and there are 365 days in one year....
-
For each of the following reactions, express the equilibrium constant: a) H20 (I) H2 (g) + 02 (g) Ke = 1.0x107 b) Fe2 (g) 2F (g) Ke= 4.9 x 10-21 c) C (s) + O2 (g) d) H2 (g) + C2H4 (g) C2H6 (g) Ke =...
-
Two objects are connected by a massless string as shown in figure. The incline and pulley are frictionless. Find the acceleration of the objects and the tension in the string for (a) General values...
-
A solid conducting cylinder of radius 0.1 m and mass of 4 kg rests on horizontal conducting rails (Figure). The rails, separated by a distance a?= 0.4 m, have a rough surface so the cylinder rolls...
-
In the "slingshot effect," the transfer of energy in an elastic collision is used to boost the energy of a space probe so that it ca n escape from the solar system. Figure shows a space probe moving...
-
Derive \(C\) and \(\phi\) to verify Equations 3.38 and 3.39 . C = x(0) - B COS (3.38) [(0) + [x(0) B]wn - Bw = tan (3.39) [x(0) - B]wd
-
For each case in Table 3.2, for the governing equation \(\ddot{x}+2 \zeta \omega_{n} \dot{x}+\omega_{n}^{2} x=A \cos \omega t\), evaluate \(C\) and \(\phi\), and \(B_{1}\) and \(B_{2}\) in Equation...
-
Derive Equations 3.44 and 3.45: \[ \begin{aligned} |G(i \omega)| & =\frac{1}{k \sqrt{\left(1-\left(\omega / \omega_{n} ight)^{2} ight)^{2}+\left(2 \zeta \omega / \omega_{n} ight)^{2}}} \\ \phi &...
Study smarter with the SolutionInn App