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MMMU-Pro / test_Mechanical_Engineering_279 / A machine tool, having a mass of m = 1000 kg and a mass moment of inertia of J0…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

A machine tool, having a mass of m = 1000 kg and a mass moment of inertia of J0 = 300 kg-m^2, is supported on elastic supports, as shown in <image 1>. If the stiffnesses of the supports are given by k1 = 3000 N/mm and k2 = 2000 N/mm, and the supports are located at l1 = 0.5 m and l2 = 0.8 m, find the natural frequencies and mode shapes of the machine tool.

img type

  • Diagrams

options

  1. $w_{1}=52.37rad/s,w_{2}=70.58rad/s$
  2. $w_{1}=92.37rad/s,w_{2}=90.58rad/s$
  3. $w_{1}=102.37rad/s,w_{2}=100.58rad/s$
  4. $w_{1}=112.37rad/s,w_{2}=110.58rad/s$
  5. $w_{1}=62.37rad/s,w_{2}=60.58rad/s$
  6. $w_{1}=122.37rad/s,w_{2}=120.58rad/s$
  7. $w_{1}=72.37rad/s,w_{2}=80.58rad/s$
  8. $w_{1}=82.37rad/s,w_{2}=70.58rad/s$
  9. $w_{1}=132.37rad/s,w_{2}=130.58rad/s$

subject

Mechanical_Engineering
image_1.png

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Source and history

upstream_id / Original problem ID
test_Mechanical_Engineering_279
task_id
6e605c2c-7e5d-5253-a357-d94eeae2e702
task_key
standard~20~2810~20options~29--test--test~5fMechanical~5fEngineering~5f279
task_revision_id
4
config / split
standard (10 options) / test

Official source

initial import