Consider the equation of motion of a simple pendulum: a. Linearize Eq. (E.1) about an arbitrary angular

Question:

Consider the equation of motion of a simple pendulum:

image text in transcribed

a. Linearize Eq. (E.1) about an arbitrary angular displacement $\theta_{0}$ of the pendulum.

b. Investigate the stability of the pendulum about $\theta_{0}=0$ and $\theta_{0}=\pi$ using the linearized equation of motion.

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

Step by Step Answer:

Related Book For book-img-for-question

Mechanical Vibrations

ISBN: 9780134361925

6th Edition

Authors: Singiresu S Rao

See More Books

Question Posted: Apr 30, 2024 03:02 AM

See More Questions

Annual revenues are currently 12.65 million and are projected to grow at 25% per annum. Assuming cost of goods sold and selling, general and administrative expenses are 49.8% and 12.2% of sales...
The data file arch.gdt contain monthly stock price indices return of U.S. Nasdaq (NR). The data are recorded monthly beginning in 1988:01 and ending in 2015:12. Question 1. i) (Bonus) Consider the...
In December 2008, Corey and Jamie Baker purchased a TV from Best Buy as well as a four-year service contract for the TV. In November 2010, Best Buy determined that the problems the Bakers were having...
Rajiv and Laurie Amin are recent college graduates looking to purchase a new home. They are purchasing a $200,000 home by paying $20,000 down and borrowing the other $180,000 with a 30-year loan...
How does cross-cultural evidence raise questions about the division of humanity into male and female?
Superheated steam at 40 bar absolute and 500C flows at a rate of 250 kg/mm to an adiabatic turbine, where it expands to 5bar. The turbine develops 1500kW. From the turbine the steam flows to a...
Main Street Bakery offers its employees the option of contributing up to 7% of their salaries to a voluntary retirement plan, with the employer matching their contribution. The company also pays 100%...
Figure 2.125 shows a uniform rigid bar of mass $m$ and length $l$, pivoted at one end (point $O$ ) and carrying a circular disk of mass $M$ and mass moment of inertia $J$ (about its...
A mass of $5 \mathrm{~kg}$ is attached to the top of a helical spring, and the system is made to vibrate by giving to the mass an initial deflection of $25 \mathrm{~mm}$. The amplitude of the...
A company has three production departments, A, B and C and two service departments, P and Q. The following figures are available as per departmental distribution summary: Production departments A B C...
Regulatory transcription factors can be modulated by a. the binding of small effector molecules. b. protein-protein interactions. c. covalent modifications. d. any of the above.
Suppose that the overexpression of a particular miRNA was associated with pancreatic cancer. Which of the following agents might be effective in treating this type of cancer? a. Enoxacin b. A DNA...
A type of secondary structure found in proteins is a. an helix. b. a sheet. c. Both a and b are secondary structures in proteins. d. Neither a nor b is a secondary structure in proteins.
Which of the following characteristics is typical of a eukaryotic gene that can be transcribed? a. The core promoter is wrapped around a nucleosome. b. The core promoter is found in a nucleosome-free...
When an ncRNA functions as a decoy, it a. contains binding sites for many different proteins, thereby promoting the formation of a large complex. b. recognizes other ncRNAs and sequesters them,...
Reconsider Prob. 1026. Now, it is proposed that the liquid water coming out of the separator be routed through another flash chamber maintained at 150 kPa, and the steam produced be directed to a...
How many years will it take a $700 balance to grow into $900 in an account earning 5%?
Before undertaking an international venture, the company should conduct a formal assessment of its readiness to internationalize. An evaluation of organizational capabilities is useful for both...
Understand the economic, social, and political issues that will affect a firm's strategy for entering specific foreign markets. Prepare a country / area size-up: Analyze relevant political, economic,...
What strategies can leaders employ to navigate the ethical quandaries inherent in decision-making processes, grappling with the ethical implications of their choices while striving to uphold...

Consider the equation of motion of a simple pendulum: a. Linearize Eq. (E.1) about an arbitrary angular

Question:

0 + sin 0 = = 0 (E.1)

Step by Step Answer:

Mechanical Vibrations

Students also viewed these Engineering questions