How can I find the amplitude of vibrations at 1250 RPM?

[wydim]

Homework Statement

a bloc of mass m=175,5 kg is supported by 2 springs K=k/2 = (unknown) and a damper c (unknown). see vibrations.bmp

at 950 RPM, a stroboscope shows that the excentric mass is at his highest and the mass m is at equilibrium position with an upward velocity.
amplitude of the vibrations is 21,5 mm
défault d'équilibrage m_o[tex]\epsilon[/tex] = 0,18 kg*m

the question is :

natural frequency ? damping factor ? amplitude of vibrations at 1250 RPM

Homework Equations

The Attempt at a Solution

I developped the equation of movement

m[tex]\ddot{x}[/tex]+c[tex]\dot{x}[/tex]+Kx = m_o[tex]\epsilon[/tex][tex]\omega[/tex]²sin([tex]\omega[/tex]t)

[tex]\omega[/tex]/[tex]\omega[/tex]_n

 

[Valkarie]

= (1-\zeta^2)^1/2\zeta = c/(2m\omegan)\omegan = sqrt(K/m)I found : natural frequency = 5,37 Hzdamping factor = 0,014But how can I find the amplitude of vibrations at 1250 RPM ?

 

[piercas]

= sqrt(1-crit2) = sqrt(1-2zeta2)

zeta = c/2m\omegan

The amplitude of vibrations at 1250 RPM can be found by using the equation of motion and solving for x. The amplitude will depend on the natural frequency, damping factor, and the initial conditions of the system.

To find the natural frequency, we can use the formula \omegan = sqrt(K/m). However, since we do not know the value of K, we cannot find the natural frequency at this time.

To find the damping factor, we can use the formula zeta = c/2m\omegan. However, we do not know the value of c or \omegan, so we cannot find the damping factor at this time.

Without knowing the values of K, c, and \omegan, it is not possible to calculate the amplitude of vibrations at 1250 RPM. More information is needed about the system, such as the values of K and c, to accurately determine the amplitude at this specific RPM.

 

[Mene]

= \sqrt{1-\zeta^2}

where \omegan is the natural frequency and \zeta is the damping factor.

To find the natural frequency, use the formula:

\omegan = \sqrt{K/m}

To find the damping factor, use the formula:

\zeta = c/2\sqrt{Km}

To find the amplitude of vibrations at 1250 RPM, use the equation:

A = A_0\omega/\omegan

where A_0 is the amplitude at 950 RPM and \omega is the angular velocity at 1250 RPM.

To find the angular velocity at 1250 RPM, use the formula:

\omega = 2\pi n/60

where n is the RPM.

Plugging in the given values, we can solve for the unknowns and find the natural frequency, damping factor, and amplitude of vibrations at 1250 RPM. We can also use these values to calculate the unknown spring constant and damping coefficient.