Question: Consider the inverted simple pendulum shown in Figure 2.66. Initially the pendulum is in a perfectly vertical position. If it is displaced very slightly from

Consider the inverted simple pendulum shown in Figure 2.66. Initially the pendulum is in a perfectly vertical position. If it is displaced very slightly from the vertical, what are the stability characteristics of the system? What kind of motion is expected and what is the equation of motion? Discuss the longterm behavior.

m 1 Figure 2.66: Inverted pendulum.

Step by Step Solution

★★★★★

3.41 Rating (148 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mechanical Vibration Analysis Questions!

A company has the following adjusted balances on December 31, 2024: Accounts Receivable $74,000; Service Revenue = $400,000; Allowance for Uncollectible Accounts $9,000; Cash = $25,000. Required:...

How do I use JAVA to code a program that will allow the user to enter the name of a student and their assignment grade, then Output the student with the highest grade

Consider the inverted pendulum shown in Figure El.13. Sketch the block diagram of a feedback control system using Figure 1.3 as the model. Identify the process, sensor, actuator, and controller. The...

PART B. DYNAMIC METHOD In this part, the spring constant & is measured using a dynamic load (a) Start with a AM of just the mass hanger. Set the mass oscillating without causing the spring to become...

This is International Business and Trade subject. Please help me answer the following (briefly and concisely): 1. Differentiate Vertical and Horizontal Foreign Direct Exchange Decisions. 2. What do...

Can someone help me by answering this exercises of a pendulum for the subject of NUMERICAL METHODS IN ENGINEERING Thanks a lot One of the fundamental systems in physics is the simple pendulum. This...

Can someone please answer the following question using MATLAB language? Can you please comment your code and post a picture of part 1 , that would be very helpful. I apologize for posting such a long...

Any part of the question complete would be helpful. I will give an amazing review, thanks!! Initials: Problem 2 - 25 points A thin rod of mass M, and length L is mounted on a frictionless vertical...

In Exercises 1 - 16, plot the point given in polar coordinates and then give three different expressions for the point such that (a) r 0 and 0 (c) r > 0 and 2 9. (20, 3) In...

Physics 161 Pendulum/Spring Lab 'Practical' Objective You will be using your experimental skills and scientific thinking. In this set of experiments, you are not going to be asked to follow specific...

Ethylene burns with 50% excess air, both entering at 25oC, 100 kPa and the product exiting at the same temperature and pressure. Determine (a) The lower heating value, (b) The higher heating value...

Smith Machining makes three products. The company's annual budget includes $1,000,000 of overhead. In the past, the company allocated overhead based on expected capacity of 40,000 direct labor hours....

Why is it important to calculate cash flow ratios? Both ( a ) and ( b ) . Companies that generate healthy profit may be unable to convert profits into cash. Firms need cash to service debt, dividends...

Can you draw up a map of the range of the international hospitality offer that is comprehensive and meaningful? Explore the difficulties in undertaking such a task.

Mode shapes of plates, by placing sand on vibrating plates, were first observed by (a) Chladni (b) D'Alembert (c) Galileo

The Philosophiae Naturalis Principia Mathematica was published by (a) Galileo (b) Pythagoras (c) Newton

The first experiments on simple pendulums were conducted by (a) Galileo (b) Pythagoras (c) Aristotle

Study the scenario and complete the questions that follow: Implementing VLSM , VLAN Interconnection, OSPF Configuration Implementing VLSM , VLAN Interconnection, OSPF Configuration, and Connectivity...

You find a stock that just paid a dividend of $1.80 that is expected to grow at 20% per year for the next four years, then at a constant rate of 6%. If you require a return of 9%, what is the most...

Elmer received a $25,000 loan from a loan shark. The loan required him to make payments of $400 per week (52 weeks per year) for three years. What annual rate (APR) and effective annual rate (EAR)...