E-CodeTwo-mass vibration: natural frequencies and mode shapes, step by step — a TI-89 Titanium program
VIB2DOF is a TI-89 BASIC program for the TI-89 Titanium. Two masses on three springs (wall, between the masses, wall). Step by step: the mass and stiffness matrices, the frequency equation det(K−ω²M)=0 expanded by the CAS, its roots, the two natural frequencies in rad/s and Hz, and the mode shape ratio X2/X1 of each mode.
What it asks for and what it shows
It asks for 5 values at its prompts. In the example below it shows ω1 rad/s, ω2 rad/s, f1=ω1/(2π) Hz, f2=ω2/(2π) Hz, r1, r2, 1 EQUATIONS OF MOTION, 2 FREQUENCY EQ (w, 5 ANSWER.
Example run
One of its oracle test cases. The inputs are typed in order, and the results are the values the case expects on the screen.
| Step | Value |
|---|---|
| You enter | |
| Input 1 | 2 |
| Input 2 | 1 |
| Input 3 | 10 |
| Input 4 | 10 |
| Input 5 | 0 |
| The screen shows | |
ω1 rad/s= | 1.711412337 |
ω2 rad/s= | 4.131714875 |
f1=ω1/(2π) Hz= | 0.2723797331 |
f2=ω2/(2π) Hz= | 0.6575828459 |
r1= | 1.414213562 |
r2= | -1.414213562 |
| Text | 1 EQUATIONS OF MOTION |
2 FREQUENCY EQ (w= | ω) |
| Text | 5 ANSWER |
How it's checked
4 test cases, each checked against an independent method. Replayed key by key on a virtual TI-89 Titanium, they make 43 checks.
How E-Code checks every program
Run it or put it on your calculator
- Open the library in the TI-89 Titanium calculator and pick “Two-mass vibration: natural frequencies and mode shapes, step by step” (VIB2DOF).
- Put it on your own calculator with a computer and a USB cable, or type it in by hand.
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All TI-89 Titanium engineering programs · All TI-89 Titanium programs