Respuesta :
Answer:
The frequency of the damped vibrations is 3.82 Hz.
Explanation:
Given that,
Spring constant = 20 lb/in
Damping force = 10 lb
Velocity = 20 in/sec
Weight = 12 lb
We need to calculate the damping constant
Using formula of damping force
[tex]b\times v=F_{d}[/tex]
[tex]b=\dfrac{F_{d}}{v}[/tex]
Put the value into the formula
[tex]b =\dfrac{10}{20}[/tex]
[tex]b=0.5\ lb-sec/in[/tex]
[tex]b=0.5\times12 =6\ lb-sec/ft[/tex]
We need to calculate the frequency
Using formula of angular frequency
[tex]\omga=\sqrt{\omega_{0}^2-(\dfrac{b}{2m})^2}[/tex]
[tex]\omega=\sqrt{\dfrac{k}{m}-(\dfrac{b}{2m})^2}[/tex]
Put the value into the formula
[tex]\omega=\sqrt{\dfrac{20\times12\times32}{12}-(\dfrac{6\times32}{2\times12})^2}[/tex]
[tex]\omega=24\ rad/s[/tex]
We need to calculate the frequency of the damped vibrations
Using formula of frequency
[tex]f=\dfrac{\omega}{2\pi}[/tex]
Put the value into the formula
[tex]f=\dfrac{24}{2\pi}[/tex]
[tex]f=3.82\ Hz[/tex]
Hence, The frequency of the damped vibrations is 3.82 Hz.
