Question

A 6.0 kilogram mass is to be suspended from a cylindrical cord made of rubber with equilibrium length 1.5 meters. If an oscillation frequency of 5 Hertz is desired when the mass is pulled so the cord stretches, what diameter should the cord have? Assume the Young’s modulus of the rubber is 2*10^6 N/m^2 , the yield stress is 3*10^6 N/m^2, and the shear modulus is 0.5*10^6 N/m^2.

Answer 1

Hi,

Hope you are doing well.

We know that,

Frequency of a SHM (Simple harmonic motion),

Where,

'' is the Force constant of rubber.(N/m)

'' is the Mass suspended.(kg)

Given that,

Frequency of a SHM,  

Mass suspended,

Also we know that,Force constant of rubber, '' is given by

Where,

'' is the Young's modulus of rubber.(N/m²)

'' is the Area of cylindrical cord.(m²)

'' is the Length of cylindrical cord.(m)

From equation (1),

Given that,

Force constant of rubber,

Length of cylindrical cord,

Young's modulus of rubber,

Area of cylindrical cord,

Area of cylindrical cord,

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