Question

A machine tool, having a mass of 1000 kg and a mass moment of inertia of J0 = 300 kg-m2 is supported on elastic supports, as shown in Figure given below. If the stiffness of the support is given by 3000 N/mm and 2000 N/mm, and the supports are located at 0.5 m and 0.8 m, find the natural frequencies.

Answer 1

$=(-1.0*10^6)/ (-1000w2 + (5*10^6)$

sub 82.3732 rad/s for w2

$=(-1.0*10^6)/-(1000)(82.732rad/s)^2 + (5*10^6)$

= 0.05601 rad/sec

hence the natural frequency

$=0.05601 rad/sec$