Free - Vibration of SDOF Mass-Spring System
Procedure
- Set parameters (m, k, c) using input controls
- Initiate motion with "Start Vibration" button
- Observe oscillations and amplitude changes
- Measure time period T for complete oscillations
- For damped systems, record peak amplitudes (x₁, x₂, x₃,...)
- Plot displacement vs. time
Analyze Results
- Compare theoretical and experimental values:
- ωₙ = √(k/m)
- ζ = c/(2√(km))
- T = 2π/ωₙ
Observations
| S.N. | Mass (m) | Stiffness (k) | Time Period (T) | Natural Frequency (ωₙ) | Damping Ratio (ζ) |
|---|---|---|---|---|---|
| 1 | |||||
| 2 |
Graphical Representation
- Displacement vs. time plots
- Amplitude decay plots for damped systems
Graph Analysis
- Underdamped (ζ < 1): Exponential decay with oscillations
- Overdamped (ζ > 1): Exponential decay without oscillations
- Critically damped (ζ = 1): Fastest non-oscillatory decay