Answer:
22.90 × 10⁸ kg
Explanation:
Given:
Diameter, d = 0.02 m
ωₙ = 0.95 rad/sec
Time period, T = 0.35 sec
Now, we know
T= [tex]2\pi\sqrt{\frac{L}{g}}[/tex]
where, L is the length of the steel cable
g is the acceleration due to gravity
0.35= [tex]2\pi\sqrt{\frac{L}{9.81}}[/tex]
or
L = 0.0304 m
Now,
The stiffness, K is given as:
K = [tex]\frac{\textup{AE}}{\textup{L}}[/tex]
Where, A is the area
E is the elastic modulus of the steel = 2 × 10¹¹ N/m²
or
K = [tex]\frac{\frac{\pi}{4}d^2\times2\times10^11}{0.0304}[/tex]
or
K = 20.66 × 10⁸ N
Also,
Natural frequency, ωₙ = [tex]\sqrt{\frac{K}{m}}[/tex]
or
mass, m = [tex]\sqrt{\frac{K}{\omega_n^2}}[/tex]
or
mass, m = [tex]\sqrt{\frac{20.66\times10^8}{0.95^2}}[/tex]
mass, m = 22.90 × 10⁸ kg
