A circular cylinder of mass 4Kg and radius 15cm is connected by spring of stiffness 4000N/m as shown in fig. Its free to roll on horizontal rough surface without slipping, determine natural frequency.

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written 7.9 years ago by

rakeshrameshpoojari • 80

modified 3.9 years ago by

Krishna_Agrawal • 2.7k

Subject:- Mechanical Vibration

Topic:- Basic Concepts of Vibration

Difficulty:- Medium

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engineering mechanics

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written 3.9 years ago by

Krishna_Agrawal • 2.7k

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Total energy of the given system -

T = Kinetic Energy due to translatory motion + Kinetic Energy due to rotatory motion + Potential Energy of spring

$T = \frac{1}{2}mx^2 + \frac{1}{2}Iθ^2 + \frac{1}{2}kx^2 $

$T = \frac{1}{2}mr^2θ^2 + \frac{1}{2}.\frac{1}{2}mr^2θ^2 + \frac{1}{2}kr^2θ^2 $

$T = \frac{1}{2}mr^2θ^2 + \frac{1}{4}mr^2θ^2 + \frac{1}{2}kr^2θ^2 …

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