Employ the events option described in Section 23.1.2 to determine the period of a 1-m long, linear
Question:
Employ the events option described in Section 23.1.2 to determine the period of a 1-m long, linear pendulum (see description in Prob. 23.10). Compute the period for the following initial conditions:
(a) θ = π / 8,
(b) θ = π / 4, and
(c) θ = π / 2.
For all three cases, set the initial angular velocity at zero.
Data from in problem 23.10
Transcribed Image Text:
23.10 The oscillations of a swinging pendulum can be sim- ulated with the following nonlinear model: d²0 d1² + sin 0 = 0 0 where = the angle of displacement, g = the gravitational constant, and I = the pendulum length. For small angular displacements, the sin is approximately equal to and the model can be linearized as d²0 dt² +0=0 Use ode45 to solve for as a function of time for both the linear and nonlinear models where 1 = 0.6 m and g = 9.81 m/s². First, solve for the case where the initial condition is for a small displacement (0 = 7/8 and de/dt = 0). Then repeat the calculation for a large displace- ment (0 = 7/2). For each case, plot the linear and nonlinear simulations on the same plot.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (5 reviews)
To determine the period of a 1meter long linear pendulum we can use the events option in MATLABs ODE ...View the full answer
Answered By
Akash M Rathod
I have been utilized by educators and students alike to provide individualized assistance with everything from grammar and vocabulary to complex problem-solving in various academic subjects. I can provide explanations, examples, and practice exercises tailored to each student's individual needs, helping them to grasp difficult concepts and improve their skills.
My tutoring sessions are interactive and engaging, utilizing a variety of tools and resources to keep learners motivated and focused. Whether a student needs help with homework, test preparation, or simply wants to improve their skills in a particular subject area, I am equipped to provide the support and guidance they need to succeed.
0.00
0 Reviews
10+ Question Solved
Related Book For
Applied Numerical Methods With MATLAB For Engineers And Scientists
ISBN: 9781259027437
3rd Edition
Authors: Steven C. Chapra
Question Posted:
Students also viewed these Mathematics questions
-
Repeat Prob. 23.11, but for the nonlinear pendulum described in Prob. 23.10. Data From Problem 23.11 Employ the events option described in Section 23.1.2 to determine the period of a 1-m long, linear...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
The cost of a can of Coca Cola in 1960 was $0.10. The exponential function that models the cost of a Coca Cola by year is given below, where t is the number of years since 1960. C(t) = 0.10e0.0576t...
-
The city of Toledo has received a proposal to build a new multipurpose outdoor sports stadium. The expected life of the stadium is 20 years. It will be financed by a 20- year bond paying 8 percent...
-
Suppose that the owner of the restaurant also wants to study the demand for dessert during the same time period. She decides that in addition to studying whether a dessert was ordered, she will also...
-
Refer to the information in Exercise 24-3 and assume instead that double-declining depreciation is applied. Compute the machines payback period (ignore taxes). (Round the payback period to three...
-
Santa Ana Services was formed on May 1, 2014. The following transactions took place during the first month. Transactions on May 1: 1. Don Humes invested $40,000 cash in the company, as its sole...
-
The half-life of a certain brand of ice cream is 180 minutes. a. Find the decay rate of the ice cream. (6 decimal places) b. How long will it take for it to decay to 60% of the original amount. c. At...
-
The following nonlinear differential equation was solved in Examples 24.4 and 24.7. Such equations are sometimes linearized to obtain an approximate solution. This is done by employing a first-order...
-
The documentation for an early version of Microsoft Word for Windows used the following for the quadratic formula. Was this correct? If not, correct it. x = b b - 4ac 2a
-
How does the purpose of merchandising, manufacturing, and service companies differ? How do they each create value?
-
A gig refers to a single project or task that an individual completes for pay, and individuals who complete gigs are often referred to as gig workers. Examples of gigs range from driving for Uber and...
-
Explain what will happen if the expectation of rising prices on New York and falling prices in London becomes widespread. Might expectations become self-fulfilling? Property investors are looking...
-
New Seasons Market is an Oregon-based grocery store chain founded in 2000 by three families who set the goal of rethinking what a grocery store could be. The store is known for offering local and...
-
After you have studied Economics in the News on pp. 204205, answer the following questions. a. What changes in the interest rate and the quantity of M2 occurred between 2007 and 2017? b. When the...
-
Costco is known as a desirable employer. This is partly because it pays an average of $21 per hour to employees in retail environments where $10.50 is the average hourly pay. Costco also covers 90%...
-
For the data for year 2003 in Exercise 7 in this section, construct a histogram, a frequency polygon, and an give, using relative frequencies.
-
In Exercises 1558, find each product. (9 - 5x) 2
-
Repeat Example 29.4 for the case where both the lower left and the upper right corners are rounded in the same fashion as the lower left corner of Figure. Note that all boundary temperatures on the...
-
With the exception of the boundary conditions, the plate in Figure has the exact same characteristics as the plate used in Examples 23.1 through 23.4. Simulate both the temperatures and fluxes for...
-
Write equations for the darkened nodes in the grid in Figure. Note that all units are cgs. The coefficient of thermal conductivity for the plate is 0.75 cal/(s cm C), the convection coefficient is...
-
A) On each of the diagram below, draw and label the forces (not components) that act on the elliptical pulley at the times indicated. To clearly indicate at which point on the pulley each force is...
-
what ways do systemic barriers impede the realization of empowerment, and how can they be effectively dismantled?
-
3. Bob holds a metal rod with a linear mass density of p at a 30 angle with the x-axis. Ann sees Bob zoom by her at a speed of 0.6c, along their common x-axis. Find the mass density of the rod as...
Study smarter with the SolutionInn App