Spring pendulum
This program can be used to study the movements of a spring pendulum. By selecting the appropriate parameters, an undamped pendulum, a damped pendulum and a periodically excited pendulum can be calculated. The oscillating pendulum is displayed together with the deflection as a function of time. In addition, a window with the associated resonance curve can be displayed. The calculation is based on the following differential equation: This program can be used to study the movements of a spring pendulum. By selecting the appropriate parameters, an undamped pendulum, a damped pendulum and a periodically excited pendulum can be calculated. The oscillating pendulum is displayed together with the deflection as a function of time. In addition, a window with the associated resonance curve can be displayed. The excitation is caused by movement of the suspension. The calculation is based on the following differential equation:
A deflection A of the suspension of a spring with the spring constant D generates a force F = D*A.
Operation
The parameters for the pendulum can be entered in the input fields. The corresponding units are indicated in each case. The deflection of the pendulum as a function of time is drawn as a red line. The deflection of the suspension as a function of time (excitation) is shown as a black line. This makes it easy to examine the phase shift between excitation and oscillation. The time t and the location x for the current cursor position are displayed at the cursor. This makes it easy to read off deflections at specific times. The resonance curve for the current parameters can be displayed at the top right by ticking "Show window". You can choose whether amplitude or phase should be displayed as a function of frequency. The currently selected case is marked as a red dot in the resonance curve. If the amplitude of the excitation is zero, there is of course no resonance and the resonance curve is identical to zero. If the parameters are changed, "Refresh" must be pressed to display the resonance curve for the new parameters.
Numerical realization: The differential equation is solved numerically using the Runge-Kutta method. A step size of 20 µs is used. The image is drawn every 20 ms.