Must solve all the questions. Dont solve partially pls. Otherwise dont attempt. A circular cylinder of mass m and radius r isconnected by a spring of stiffness k and a damper ofdamping constant c as shown in Figure 1. If it is freeto roll on the rough horizontal surface withoutslipping, the rotary inertia of the cylinder isJ, =-mr, and the rotational angle is 6.(1) Draw the free body diagram for the cylinder.(2) Derive the equation of motion of the systemusing Newton's 2nd law.(3) Determine the undamped natural frequency of the system.Will the damped period be doubled when the damping constant is doubled? Explain why.Figure 1

Given Data The mass of cylinder is:m The radius of cylinder is:r The spring stiffenss is:k The…

A circular cylinder of mass m and radius r is connected by a spring of stiffness k and a damper of damping constant c as shown in Figure 1. If it is free to roll on the rough horizontal surface without slipping, the rotary inertia of the cylinder is

A circular cylinder of mass m and radius r is connected by a spring of stiffness k and a damper of damping constant c as shown in Figure 1. If it is free to roll on the rough horizontal surface without slipping, the rotary inertia of the cylinder is

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Must solve all the questions. Dont solve partially pls. Otherwise dont attempt.

A circular cylinder of mass m and radius r is
connected by a spring of stiffness k and a damper of
damping constant c as shown in Figure 1. If it is free
to roll on the rough horizontal surface without
slipping, the rotary inertia of the cylinder is
J, =-mr, and the rotational angle is 6.
(1) Draw the free body diagram for the cylinder.
(2) Derive the equation of motion of the system
using Newton's 2nd law.
(3) Determine the undamped natural frequency of the system.
Will the damped period be doubled when the damping constant is doubled? Explain why.
Figure 1

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