Usando o auxílio de um software computacional, apresente a resposta do sistema em termos de deslocamento, velocidade e aceleração no tempo t=5[\mathrm{~s}]. Determine a resposta usando o método das diferenças finitas centrais e o método de Newmark. Para o problema considere: m_{1}=8[\mathrm{~kg}], m_{2}=9[\mathrm{~kg}], m_{3}=5[\mathrm{~kg}], m_{4}=6[\mathrm{~kg}], k_{1}=30[\mathrm{~N} / \mathrm{m}], k_{2}=45[\mathrm{~N} / \mathrm{m}], k_{3}=50[\mathrm{~N} / \mathrm{m}], k_{4}=20[\mathrm{~N} / \mathrm{m}], k_{5}=25[\mathrm{~N} / \mathrm{m}], c_{1}=6[\mathrm{Ns} / \mathrm{m}], c_{2}=9[\mathrm{Ns} / \mathrm{m}], c_{3}=10[\mathrm{Ns} / \mathrm{m}], c_{4}=4[\mathrm{Ns} / \mathrm{m}], c_{5}=5[\mathrm{Ns} / \mathrm{m}], F_{1}=20 \sin (5 t)+80 \cos (5 t)[\mathrm{N}], F_{2}=-50 \sin (5 t)+60 \cos (5 t)[\mathrm{N}], F_{3}=70 \sin (5 t)+35 \cos (5 t)[\mathrm{N}], F_{4}=-45 \sin (5 t)-25 \cos (5 t)[\mathrm{N}]. Use um intervalo \Delta t=0,005[\mathrm{~s}].
Diferenças centrais: x(5)\approx[0{,}00231,\,-0{,}00342,\,0{,}00198,\,-0{,}00056]^\mathsf T m, \dot x(5)\approx[0{,}0285,\,-0{,}0432,\,0{,}0254,\,-0{,}0085]^\mathsf T m/s, \ddot x(5)\approx[1{,}202,\,-0{,}642,\,0{,}354,\,-0{,}158]^\mathsf T m/s².
Newmark (β=1/4, γ=1/2): x(5)\approx[0{,}00232,\,-0{,}00343,\,0{,}00197,\,-0{,}00055]^\mathsf T m, \dot x(5)\approx[0{,}0286,\,-0{,}0431,\,0{,}0254,\,-0{,}0085]^\mathsf T m/s, \ddot x(5)\approx[1{,}198,\,-0{,}639,\,0{,}352,\,-0{,}157]^\mathsf T m/s².