Answer:
[tex]E=8.69J[/tex]
Explanation:
The total energy of a mass-spring system is defined as:
[tex]E=\frac{kA^2}{2}(1)[/tex]
Where k is the spring constant and A is the amplitude of the oscillation. We can calculate k from the natural frequency of this system:
[tex]\omega^2=\frac{k}{m}\\k=m\omega^2(2)[/tex]
Now, we can calculate [tex]\omega[/tex] from the maximum acceleration:
[tex]a_{max}=A\omega^2\\\omega^2=\frac{a_{max}}{A}(3)[/tex]
Replacing (3) in (2):
[tex]k=m\frac{a_{max}}{A}[/tex]
Replacing this in (1):
[tex]E=\frac{ma_{max} A^2}{2A}\\E=\frac{ma_{max}A}{2}\\E=\frac{5.7kg(9.3\frac{m}{s^2})(32.8*10^{-2}m)}{2}\\E=8.69J[/tex]
