Question: Consider the free motion of a plane pendulum whose amplitude is not small. Show that the horizontal component of the motion may be represented by

Consider the free motion of a plane pendulum whose amplitude is not small. Show that the horizontal component of the motion may be represented by the approximate expression (components through the third order are included).

Where w2/0 = g/l and ε = 3g/2l3, with l equal to the length of the suspension.

* + wi1 + ex3 = 0

Step by Step Solution

★★★★★

3.43 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let us start with the equation of motion for the simple pendulum o sin where gl ... 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)

P-C-D-N-O (11).docx

120 KBs Word File

Students Have Also Explored These Related Classical Dynamics Of Particles Questions!

A driver and car may be represented by the simplified model shown. The goal is to have the speed adjust to a step input with less than 10% overshoot and a settling time (with a 2% criterion) of 1...

Each of the following may be represented by at least one alternative resonance structure in which all the six-membered rings correspond to Kekulé forms of benzene. Write such a resonance form...

Consider a simple pendulum of length L that has a small mass (the bob) of mass m attached to the end of its string. If the pendulum starts out horizontally and is released from rest, show that (a)...

Calculus 3 Sections 12.1 and 12.2 Reading Assignment: 3D Coordinates and Vectors Answer Only Exercise 1 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three...

Part A: Centripetal Force . 445kg Mass of bob: 445, Radius of Revolution: 17 cm Time for 25 Revolution Period: 18.15/ 25= ,726 Revolutions: 18+ 13 5 Computed Centripetal Force: J 2 10 , 726 )2...

(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...

Note: To simplify calculations, you may use g = 10 m/s in all problems.V =7.5 m/s Questions 2-4 refer to the following figure: B C - NWAVAN D velocity (m/s) 1. An object is thrown horizontally to the...

space weather PLEASE HELP ME use MATLAB NO REFERENCE 1.1 Free Space Maxwell's equations describe the behavior of electromagnetic fields and their interaction with mat- ter. They are one of the major...

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...

software projects failed. In the run-up to Y2K, most of the world's large companies claimed that fixing the Millennium Bug was a large project whose success was critical to their survival. One would...

In the picture given, moist air properties for an HVAC unit are seen. Examine the numbers and explain why there is at least one value that is incorrect ( a value that doesn't make sense) Humidity...

Multiple Choice Question 1. Which of the following is not management accounting information? A. Sales budget B. Variance report C. Payroll report D. Profitability report 2. Why is management...

Suppose the temperature inside your winter home is 6 8 F at 1 0 : 0 0 A . M . and your furnace fails. If the outside temperature is 2 0 F and you notice that by 2 : 0 0 P . M . the inside temperature...

Two students are each given a spherical balloon that has a long string attached and is filled with an unknown gas whose density is referred to by the variable PG. The filled balloons each have a...

Fill out the market analysis worksheet based on the following information. The Subject property is located in Sweetbriar subdivision at 144 Sweetbriar Trail. It is an eight room, one story, wood...

The Oriole Hotel opened for business on May 1, 2022. Here is its trial balance before adjustment on May 31. ORIOLE HOTEL Trial Balance May 31, 2022 Cash Supplies Prepaid Insurance Land Buildings...

Post the adjusting entries to the ledger accounts. Enter the totals from the trial balance as beginning account balances. (Use T-Accounts.) (Post entries in the order of journal entries presented in...

Use cost structure concepts (ie fixed costs, variable costs, semi variable costs mixed costs, and step costs step fixed costs) to answer the following questions Suppose the community college wants to...

Discuss the practical issues to be considered by a company when deciding on the size of its dividend payment.

You can purchase an optical scanner today for $400 The scanner provides benefits worth $60 a year The expected We of the scanner is 10 years Scanners are expected to decrease in price by 20% per year...

please do this question Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns. a. What are the betas of the two stocks? (Round...

Prove that the given argument is valid. First find the form of the argument by defining predicates and expressing the hypotheses ar the conclusion using the predicates. Then use the rules of...