Forced Vibration
Calculates a table of displacement for damped oscillation driven by an external force and plots the results.
Displays a graph over 4 periods of the driving oscillation.
| \(\\ \hspace{20px}{\large\frac{d^2 x}{dt^2}}+2\kappa{\large\frac{dx}{dt}}+{\omega_{\small 0}}^2 x=f\cdot cos(\omega t)\\\) |
| \(\normalsize Forced\ Oscillation\\ (1)\ equation\\ \hspace{25px} {\large\frac{d^2 x}{dt^2}}+2\kappa{\large\frac{dx}{dt}}+{\omega_{\small 0}}^2 x=f\cdot cos(\omega t)\\ \hspace{35px}\omega_{\small 0}:\ undamped\ angular\ frequency\\ \hspace{40px}\kappa:\ resistance\ coefficient\\ \hspace{40px}f:\ driving\ amplitude\\ \hspace{40px}\omega:\ driving\ frequency\\ (2)\ x=A\cos(\omega t-\delta)\\ \hspace{25px}A={\large\frac{f}{({\omega_{\small 0}}^2-\omega^2)+(2\omega\kappa)^2}}\\ \hspace{25px}\tan\delta={\large\frac{2\omega\kappa}{{\omega_{\small 0}}^2}-\omega^2}\\ \) |
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