Question

A machine of mass 500kg is mounted through four rubber mountings that exhibit linear elasticity and viscous damping.in the installation of the machine ,each pad was observed to undergo a compression of 15mm. During the trial run of the machine ,the system was observed to execute free samples vibration such that it made 50 oscillations in 15 seconds.For this system,find;

a)the stiffness and damping coefficient of each mounting.

b)the minimum number of oscillations and consequently the time it will take for the amplitude of oscillations to be reduced to 1%.

Answer 1

number of oscillations = 50

time taken for oscillations = 15s

angular frequency = 50/15 = $3.3s^{-1}$

X_max = 15mm = $15×10^{-3}m$

mass = 500kg

$k = \dfrac{m_o \omega^2}{X(1-r²)}$

$k =\dfrac{500×10²}{3²×15×10^{-3}×{1-0.01²}}$

$=370\ kN/m$