Solve Problem 4.82 (using Runge-Kutta method) for the forcing function [F(t)= begin{cases}F_{0} sin frac{pi t}{t_{1}} ; &
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Solve Problem 4.82 (using Runge-Kutta method) for the forcing function
\[F(t)= \begin{cases}F_{0} \sin \frac{\pi t}{t_{1}} ; & 0 \leq t \leq t_{1} \\ 0 ; & t \geq t_{1}\end{cases}\]
with \(F_{0}=2000 \mathrm{~N}\) and \(t_{1}=6 \mathrm{~s}\).
Data From Problem 4.82:-
Find the response of a damped single-degree-of-freedom system with the equation of motion \[m \ddot{x}+c \dot{x}+k x=F(t)\]
using Runge-Kutta method. Assume that \(m=5 \mathrm{~kg}, c=200 \mathrm{~N}-\mathrm{s} / \mathrm{m}, k=750 \mathrm{~N} / \mathrm{m}\), and \[F(t)= \begin{cases}\frac{F_{0} t}{t_{1}} ; & 0 \leq t \leq t_{1} \\ F_{0} ; & t \geq t_{1}\end{cases}\]
with \(F_{0}=2000 \mathrm{~N}\) and \(t_{1}=6 \mathrm{~s}\).
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