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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.

Subject:- Mechanical Vibration

Topic:- Basic Concepts of Vibration

Difficulty:- Medium


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1 Answer
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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=12mx2+12Iθ2+12kx2

T=12mr2θ2+12.12mr2θ2+12kr2θ2

T=12mr2θ2+14mr2θ2+12kr2θ2

T=34mr2θ2+12kr2θ2=constant

Differentiating T with respect to time we get,

0=34.2mr2θ+kr2θ=0

i.e.=32mr2θ+kr2θ=0

Ω(n)=kr23/2mr2

i.e.=2k3mrad/sec

f(n)=12π2400034m=4.11Hertz(Hz)

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