Imagine modeshape and find eigenfrequency by back of envelope calculation

My lecturer likes to do this thing where he wants us to be able to imagine the modeshape and "guess" the eigenfrequencies of a given mass spring damper system, but really gives little details on how we can do this. For the attached system (m1 = 2500 kg, m2=320 kg, k1=80000, k2=500000, ignore the dampers) , I can somewhat imagine that the modes would be m1 and m2 moving together in same direction and the other moving in opposite direction. But is that all? How do I know that's all? In addition, he wrote that the first eigenfrequency is approximately sqrt(k1/m1) by back of envelope calculation. Is it because m1 is heaviest? Is there any general procedure for doing this? Example system (damping is ignored) ​ submitted by /u/aldosebastian [link] [comments]

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