A three-storey frame, swaying in slow motion.
The MDOF (multiple degree of freedom) free-vibration problem, taken apart frame by frame: how stiff each storey is, why the eigenvalue problem appears, where the three mode shapes come from, and what the building actually does when you let go of it. Change any number below and the whole story re-solves.
Watch the solution build itself
Ten short chapters, one idea each. Press play and it advances on its own, or step through with the arrows. Everything on screen is computed from the numbers in the model — nothing is hard-coded.
Everything the question asks for
Same numbers as the tour, in one place — the stiffness of a column and of each storey, the natural frequencies and periods, and the mode shapes. They update the moment you change the model.
Storey stiffness
Frequencies & periods
Mode shapes
Mass and stiffness matrices
Checks
On your calculator
Change anything, watch it re-solve
The lesson only covers two- and three-storey frames, so those are the two you get — but every other number is yours: concrete strength, column size, number of columns, storey heights, floor masses, and how the building is set in motion.
Method, matrices and checks
If you want to reproduce this by hand or in code, everything is here: the exact matrices, the polynomial, the back-substitution formulas and the identities used to verify the numbers.