Answer:
1).[tex]T=0.314sec[/tex]
2).[tex]y'(t)=21.24ft/s[/tex]
3).[tex]y(t)=10*sin(16.66*t)[/tex]
Explanation:
1.
Time of the oscillation of the vertical motion of the car is
[tex]T=2*\pi *\sqrt{\frac{m}{K}}[/tex]
[tex]T=2*\pi *\sqrt{\frac{2000}{25000*32}} =2\pi *0.05[/tex]
[tex]T=0.314sec[/tex]
2.
After 10 sec the car is at the high point of it's
[tex]y(0)=1.0 ft[/tex]
[tex]y(t)=-A*cos(wt)[/tex]
[tex]y'(t)=A*w*sin(wt)[/tex]
[tex]w=\frac{2\pi}{T}=16.66rad/s[/tex]
[tex]y'(t)=62.05*sin(20.0181)[/tex]
[tex]y'(t)=21.24ft/s[/tex]
3.
Coefficient r'
[tex]r=\frac{6.93}{2*m}[/tex]
[tex]r=0.0554[/tex]
[tex]w'=\sqrt{w_o^2-r^2}=\sqrt{16.67^2-0.5544^2}[/tex]
[tex]W'=16.66sec^{-1}[/tex]
[tex]y(0)=0[/tex]
[tex]y(t)=A*sin(w't)[/tex]
[tex]y(t)=10*sin(16.66*t)[/tex]
