The animation compares the oscillation behavior of two spring-mass systems: one without damping (harmonic oscillation) and one with damping (damped oscillation). Amplitude, frequency, and damping constant can be varied interactively, while the resulting motions are displayed both mechanically and in a time diagram.
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Description of the Animation
The animation visualizes two fundamental types of mechanical oscillations side by side:
Undamped oscillation (blue): The mass oscillates with constant amplitude around its equilibrium position. The motion follows the equation:
\[ y(t) = -A \cdot \cos(\omega t) \]
Damped oscillation (red): Due to frictional forces, the amplitude decreases exponentially. The motion is described by:
\[ y(t) = -A \cdot e^{-\delta t} \cdot \cos(\omega t) \]
Here, \( A \) is the initial amplitude, \( \omega = 2\pi f \) is the angular frequency, and \( \delta \) is the damping constant.
The left area of the animation shows the two spring-mass systems. The springs are drawn dynamically and adapt to their respective displacement. The right area displays a coordinate system showing the time evolution of both oscillations. The dashed envelope \( \pm A \cdot e^{-\delta t} \) illustrates the exponential amplitude decay of the damped oscillation. Horizontal connecting lines between the masses and the curve markers allow direct correlation of the mechanical motion to the diagram.
Interactive Controls
The animation offers several interaction options:
- Amplitude A: Determines the maximum displacement from the equilibrium position (20 to 120 pixels). Both oscillations start with this amplitude.
- Frequency f: Controls the oscillation frequency from 0.1 to 2.0 Hz. The period \( T = 1/f \) is shown in the current values display.
- Damping δ: Controls the strength of damping from 0 to 2. At δ = 0, the red oscillation also behaves undamped; at high values, it decays quickly.
- Start/Pause: Starts or pauses the animation. The simulation runs over a time span of 10 seconds.
- Reset: Resets the time to zero and restarts the display.
The lower left area shows the current values: time \( t \), the instantaneous displacements \( y_1 \) and \( y_2 \), and the period \( T \).
Overview
| Title | Damped mass-spring system |
| Target Audience | Teachers and Lecturers |
| License | Open Source – CC BY 4.0 |
| Attribution Notice | Created with AI assistance |