Question

A 350 kg mass, constrained to move only vertically, is supported by two springs, each having a spring constant of 250 kN/m. A periodic force with a maximum value of 100 N is applied to the mass with a frequency of 2.5 rad/s. Given a damping factor of 0.125, the amplitude of the vibration is

Answer 1

Step-by-step explanation:

Expression for amplitude of forced damped oscillation is as follows

A =
`(F_0)/(√(m(\omega^2-\omega_0^2)^2+b^2\omega^2) )`

where

ω₀ =
`\sqrt{(k)/(m) }`

ω₀ =
`\sqrt{(500000)/(350) }`

=37.8

b = .125 ,

ω = 2.5

m = 350

A =
`(100)/(√(350(37.8^2-2.5^2)^2+.125^2*2.5^2) )`

A = 3.75 mm . Ans