Question

A torsional pendulum has a natural frequency of 200 cpm in vacuum. The mass moment of inertia is 250 kg/m2. It is immersed in oil and its natural frequency is found to be 170 cpm.

Answer 1

Answer:

The value of damping factor of the oil is 0.67

Explanation:

Equation for the damping factor calculation is ;

Fd/Fn = cos ( 1- ζ^2)

Where Fd is the damped frequency, Fn the natural frequency and ζ is the damping factor that we need to find out in our case;

( 1- ζ^2) = cos^(-1)⁡〖Fd/Fn〗

The value of damping factor of the oil

ζ = √(1-cos^(-1)⁡〖Fd/Fn〗 )

Now putting the values;

ζ = √(1-cos^(-1)⁡〖170/200〗 )

ζ = 0.67