Find the characteristic frequencies of the system

Reference no: EM13257585

Three balls are constrained to move on the circumference of a circle of radius R. The balls are connected to each other along the circumference of the circle by three identical springs with spring constant k so that in the equilibrium configuration, the springs all have their common rest length, and the balls are spaced evenly around the circle. The mass of the first ball is M; the other two balls have mass m, m<M.

a) Choose as coordinates the angles a1, a2, and a3, the angular displacements of the three balls from the equilibrium configuration. Derive the Euler-Lagrange equations for the system in terms of these angles.

b) Using the result of part a, find the characteristic frequencies of the system.

c) What happens if m=M?

Reference no: EM13257585

Questions Cloud

Find the distance the sled moves before it stops : A sled of mass m is given a kick on a frozen pond. The kick imparts to it an initial speed of 1.60 m/s. The coefficient of kinetic friction between sled and ice is 0.110. Use energy considerations to find the distance the sled moves before it stop..

Searching library research databases : Identifying scholarly resources, such as peer-reviewed journal articles and searching library research databases (general or subject-specific)

What is the purpose of closing the books : What is the purpose of closing the books? After closing, what is the amount of owner's equity that will be reported on the balance sheet?

Present value of the receivable on biotech books : Compute the present value of the receivable on Biotech's books for January 1, 2006 immediately after receiving the $1million down payment.

Find the characteristic frequencies of the system : Three balls are constrained to move on the circumference of a circle of radius R. find the characteristic frequencies of the system

What was the sticker price of the car : What was the sticker price of the car if the monthly interest rate is 1.5% (periodic rate) and it takes 4 years (48 months) to pay off the car?

Explain how you could use breakeven analysis : Explain how you could use breakeven analysis to determine your bid amount on the proposal. Use the Profit Model to demonstrate your response. Ensure you include a well considered discussion of the revenue and expenses.

What is the new motor speed of induction machine : we know Ktw=1 Nm(rad/s) and its's rated torque 30Nm for the synchronous frequency 60 H. If this motor is running at 60Hz, its load torque changes from 30 to 10 Nm, what is the new motor speed.

Six different transactions : Indicate how each of the following six different transactions that Dynamic Mattress might make would affect (i) cashand (ii) net working capital:

User Account

All Pages