The mass of a single degree damped system is 8 kg and makes 28 free oscillations in 16 secs. TheAmplitude however reduces to 0.3 of its initial value after 5 complete oscillations.

Determine:

i. Stiffness of the spring

ii. Logarithmic decrement

iii. Damping factor.

Given : m = 8 kg

Since 28 oscillations are made in 16 seconds, therefore frequency of free vibrations, fn = 28/16 = 1.75 and $$ \begin{array}{r} \omega_{n}=2 \pi \times f_{n}=2 \pi \times 1.75 \\ =11 \mathrm{rad} / \mathrm{s} \end{array} $$

1.Stiffness of the spring

Let s = stiffness of …