Find normal frequencies and forms of normal modes

Assignment Help Mechanical Engineering

Reference no: EM131383162

A particle P of mass 3m is suspended from a fixed point O by a light inextensible string of length a. A second particle Q of mass m is in turn suspended from P by a second string of length a. The system moves in a vertical plane through O. Show that the linearised equations of motion for small oscillations near the downward vertical are

4θ^·· + Φ^·· + 4n²θ = 0,

θ^··+ Φ^··+ n²Φ = 0,

where θ and Φ are the angles that the two strings make with the downward vertical, and n² = g/a. Find the normal frequencies and the forms of the normal modes for this system.

Reference no: EM131383162

Questions Cloud

Examine the character of pearl in the scarlet letter : Examine the character of Pearl in the Scarlet Letter. How does she function as a symbol in the novel? Do you find her character convincing? Why or why not

Examples of business processes or operations : 1) Give three examples of business processes or operations that would benefit significantly from having detailed real-time or near real-time data and identify the benefits.

Create a variable named name by assigning your name : Create a variable named ‘Name' by assigning your name. Create a variable named ‘Surname' by setting your surname properly. Create a variable of scalar named ‘Cnumber' by assigning your number.

Diffusion of innovation-discussion : Chocoberry, our You Decide from previous weeks, decided to launch new retail chocolate products that would claim lower calories, high antioxidants, and other similar benefits. How does this value proposition relate to the diffusion of innovations c..

Find normal frequencies and forms of normal modes : A particle P of mass 3m is suspended from a fixed point O by a light inextensible string of length a.- Find the normal frequencies and the forms of the normal modes for this system.

Does this film or website depict the country accurately : Refer to the film or website you identified in Module 3 about the country you have chosen for your Portfolio Project. Summarize the website or the film and describe the important information presented. Does this film or website depict the country ..

Industry influences activity context : Evaluate an organization's strategic fit with the external industry environment. Communicate in a manner that is professional and consistent with expectations of members of the business professions.

Entering a number of items and calculating sales tax on sale : Entering a number of items and calculating sales tax on a sale; include a step offering a warranty for each item. Converting from Fahrenheit to Celsius or the reverse over temperatures for several days

Unskilled labor or apprentices : Minimum wages are normally associated with unskilled labor or apprentices. Because you support fair trade and local, sustainable, and organic products, you feel compelled to be fair to your less skilled staff and decide to pay them above minimum w..

User Account

All Pages