Answer:
[tex]E=36.64J[/tex]
Explanation:
The total mechanical energy of a mass-spring system is defined as:
[tex]E=\frac{kA^2}{2}[/tex]
Here k is the spring constant and A is the amplitude of the oscillations.
We can calculate the spring constant using the natural frequency of this system:
[tex]\omega^2=\frac{k}{m}\\k=m\omega^2[/tex]
Recall that [tex]\omega=2\pi f[/tex], so:
[tex]k=m(2\pi f)^2\\k=2.5kg(2\pi*3Hz)^2\\k=888.26\frac{N}{m}[/tex]
Finally, we calculate E:
[tex]E=\frac{888.26\frac{N}{m}(8.25*10^-2m)^2}{2}\\E=36.64J[/tex]
