Answer:
[tex]u(t)=\frac{15}{7}*sin(14t)[/tex]
Explanation:
Given
[tex]m=100g[/tex]
[tex]L=5cm[/tex]
[tex]u(0)=0[/tex]
[tex]u(0)'=30\frac{cm}{s}[/tex]
The function that describe the motion is:
[tex]u(t)=A*cos(wt)+b*sin(wt)[/tex]
[tex]w_{o}^2=\frac{g}{L}[/tex]
[tex]w_{o}^2=\frac{9.8\frac{m}{s^2}}{0.05m}[/tex]
[tex]w=\sqrt{196\frac{m^2}{s^2}}=14\frac{m}{s}[/tex]
[tex]u(t)=A*cos(14t)+B*sin(14t)[/tex]
[tex]u(0)=0+30=B*sin(14)[/tex]
[tex]14B=30[/tex]
[tex]B=\frac{15}{7}[/tex]
[tex]u(t)=\frac{15}{7}*sin(14t)[/tex]
