Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Consider the mechanical system shown on the right. A mass m slides on a surface with viscous friction b, and a spring with stiffness

Consider the mechanical system shown on the right. A mass m slides on a surface with viscous friction b, and a spring with stiffness k is connected between the mass and a wall on the left. The coordinate x Io No gravity, g = 0. denotes the horizontal position of the mass, and x = 0 is the rest position of the spring. The mass is connected to the end of a thin rod via a rigid, inextensible T-bar. The thin rod of length L pivots about point 0, and has moment of inertia lo about the pivot. The angle 0 denotes the counter-clockwise angle of the rod from the vertical; you may assume that the spring is at rest when 0 = 0 (that is that x = 0 when 0 = 0). A horizontal, rightward-pointing input force u(t) is applied at the midpoint of the rod (at length L/2 down the rod). The T-bar connection between the mass and the u(t) k end of the rod simply makes sure that any force transferred between the mass and the rod is purely horizontal. The left side of the T-bar slides up and down in a frictionless groove in the mass m, and the right side is connected to a frictionless pivot on the end of the rod (at length L down the rod). m viscous friction, b Derive the equation of motion (EOM) for this dynamic system. Assume that there is no gravity, but do not make any small-angle approximations.

Step by Step Solution

3.51 Rating (175 Votes )

There are 3 Steps involved in it

Step: 1

Solution Solution a In addition to the coordinate 0 identified in the original figure we a... blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image_2

Step: 3

blur-text-image_3

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Vector Mechanics for Engineers Statics and Dynamics

Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell

8th Edition

73212229, 978-0073212227

More Books

Students also viewed these Mechanical Engineering questions

Question

please dont use chat gpt AI 4 2 0 . CSTR .

Answered: 1 week ago

Question

What is job enlargement ?

Answered: 1 week ago

Question

what is the most common cause of preterm birth in twin pregnancies?

Answered: 1 week ago

Question

Which diagnostic test is most commonly used to confirm PROM?

Answered: 1 week ago

Question

What is the hallmark clinical feature of a molar pregnancy?

Answered: 1 week ago