A pendulum with a stiff arm (like a pen swinging from its tail) has two equilibrium...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A pendulum with a stiff arm (like a pen swinging from its tail) has two equilibrium points. A stable one where the tip of the pen is down, close to the surface of the Earth, and an unstable equilibrium point where the tip of the pen is up, i.e., moving far from the surface of the Earth compared to its tail. In the latter case, small oscillation around the top points are described by the equation d0 dt2 (2) where w is a constant angular frequency. Show that the solution to this differential equation is I 0 = A cosh (wt) + B sinh (wt), (3) = w0. A pendulum with a stiff arm (like a pen swinging from its tail) has two equilibrium points. A stable one where the tip of the pen is down, close to the surface of the Earth, and an unstable equilibrium point where the tip of the pen is up, i.e., moving far from the surface of the Earth compared to its tail. In the latter case, small oscillation around the top points are described by the equation d0 dt2 (2) where w is a constant angular frequency. Show that the solution to this differential equation is I 0 = A cosh (wt) + B sinh (wt), (3) = w0.
Expert Answer:
Answer rating: 100% (QA)
where A and B are constants that depend on initial conditions To show that the solution to ... View the full answer
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
Posted Date:
Students also viewed these mathematics questions
-
Design a Java class that represents a cache with a fixed size. It should support operations like add, retrieve, and remove, and it should evict the least recently used item when it reaches capacity.
-
a. Example 13-1: Batch Reactor with an Exothermic Reaction Wolfram 1. Adiabatic Case: Use Wolfram to see whether you can find a trajectory that is ready to ignite and whose trajectory looks like a...
-
A New York Times editorial argued that college students are taken advantage of by credit card companies: The credit card industry has made a profitable art of corralling consumers into ruinous...
-
Define, describe and identify the elements of (a) good Data Backup Planning, (b) good Disaster Recovery Planning, and (c) good Business Continuity Planning. Be sure to identify and describe any...
-
Assume that Little King Sandwiches uses straight-line depreciation and University Hero uses double-declining-balance depreciation. Explain the difficulties in comparing the income statements and...
-
A lot of compensation information is available to employees today on the Web (e.g., www.salary.com), and much of it is inaccurate. How can an organization assure employees that they are fairly...
-
Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.76.You believe that the figure is higher in your area of the country. You decide to test this...
-
Allocate overhead using a single plantwide rate, multiple department rates, and activity-based costing Downhill Sports Inc. manufactures two products: snowboards and skis. The factory overhead...
-
Yang Specialty Products has a generous return policy. Yang gives customers a 30-day trial period, after which they can return the product for a full refund if not satisfied. Under what conditions can...
-
On January 1st, Yves purchased a $10,000, 180-day Government of Canada T-bill maturing on June 29th at a quoted yield of 2.77%. On March 15th, he sells the T-bill for $9,872. What is Yves' taxable...
-
Explain how buyers and sellers factor into setting the stock price for a company's shares. Explain brielfy with the help of examples.
-
The last investment option for BIC is a run-down building on 1 acre of land called Crystal Estates. They expect to rent the building as a storage facility, which will yield an NOI of $105,000 next...
-
Suppose an international conflict results in a jump in the price of oil. The jump causes investors to raise their expected rate of inflation, and the risk-free rate increases from 3.0 to 4.0 percent...
-
What is Intel Corporation's firm Position - you need to document the position of the firm within the context of the industry based on news reports, management discussion as well as analysts' reports...
-
1. Social Security benefits stress individual equity rather than social adequacy. 2. The Banking Act of 1933, known as the Glass-Steagall Act, effectively kept commercial banks out of the commercial...
-
Khan Borrows 20,000 from Zarak and promises to pay after two months. Draft a relevant note for giving payment. Also list down the essential elements of promissory note.
-
Why is disclosure of depreciation or amortization methods and rates so important?
-
1. Cancellation Works Prove using matrix algebra that if A, 8, and C are matrices such that AB = AC, and A is invertible, then B = C? 2. An Inverse Prove that if A is invertible and B is another...
-
lnvertibility In Problems 1-3, What choices of k and m would make the matrices invertible? Check the determinant. 1. 2. 3. Invertibility Test: In Problems 1-3, use the determinations of the matrices...
-
When a one-parameter family of curves satisfies a first-order DE, we can find another such family as solution curves of a related DE with the property that a curve of the other family orthogonally....
-
Describe what sexual harassment is and what forms it can take.
-
Describe what is meant by retaliatory and constructive discharge and how to defend a claim for unfair discharge.
-
Explain public policies that protect employees from unlawful discharge.
Study smarter with the SolutionInn App