The code seems to work fine but why don't the frequencies work out? When m1=m2=m and k1=k3=k the normal modes w1=sqrt(k/m) and w1=sqrt((k+2k2)/m). For the values in he code k=10, k2=5, m=0.15 w1=8.1 w2=11.5. The code yields frequencies of approximately w1=1.3, w2=1.8
If we assume a normal mode, the solution will have the same as simple harmonic motion - so picking e^iwt works (with a constant as the vector). When you take the derivative twice, you get the same thing back with a constant. Here's a blog post on this - that might help too rjallain.medium.com/the-physics-of-coupled-oscillators-ce2005f9bccd
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2:04 for 2nd normal mode, the two masses and the middle spring move like on rigid body, thanks for the animation.
The code seems to work fine but why don't the frequencies work out? When m1=m2=m and k1=k3=k the normal modes w1=sqrt(k/m) and w1=sqrt((k+2k2)/m). For the values in he code k=10, k2=5, m=0.15 w1=8.1 w2=11.5.
The code yields frequencies of approximately w1=1.3, w2=1.8
Both entertaining and instructive, thank you!
Glad you enjoyed it!
its a fantabulous explanation sir!!!!!!!!!!
Thanks and welcome
Beautiful explanation. Thank you.
Glad you liked it!
Keep it up!
11:30
How did e⁻ⁱʷᵗ appear? I didn't understand why it appeared multiplying on the matrix side
If we assume a normal mode, the solution will have the same as simple harmonic motion - so picking e^iwt works (with a constant as the vector). When you take the derivative twice, you get the same thing back with a constant.
Here's a blog post on this - that might help too rjallain.medium.com/the-physics-of-coupled-oscillators-ce2005f9bccd
pog
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