[tex]v_{f}=1.0644 m/s[/tex]
Explanation:
According to law of conservation of energy:
Total initial Energy= Total Final Energy
[tex]E_{0} = E_{f}[/tex]
[tex]\frac{1}{2}*mv_{0} ^{2}+\frac{1}{2}*kx_{0} ^{2}=\frac{1}{2}*mv_{f} ^{2}+\frac{1}{2}*kx_{f} ^{2}[/tex]
In above expression
[tex]v_{0}=0[/tex] (System is initially at rest)
So above expression will become:
[tex]\frac{1}{2}*kx_{0} ^{2}=\frac{1}{2}*mv_{f} ^{2}+\frac{1}{2}*kx_{f} ^{2}[/tex]
BY rearranging the above expression we will get final velocity/Speed:
[tex]v_{f}=\sqrt{\frac{k}{m}}*\sqrt{x_{0} ^{2}-x_{f} ^{2}}[/tex]
[tex]v_{f}=w*\sqrt{x_{0} ^{2}-x_{f} ^{2}}[/tex]
[tex]v_{f}=15.3*\sqrt{(-0.077)^{2}-(0.033)^{2}}[/tex]
[tex]v_{f}=1.0644 m/s[/tex]
