Answer
$E=1.2J$
Work Step by Step
The total energy of a mass-spring system can be expressed as the total elastic potential energy or kinetic energy. For this question, the kinetic energy formula will be used. This is $$K=E=\frac{1}{2}mv_{max}^2$$ Remember that the maximum velocity can be expressed as $v_{max}=A\omega$. The angular frequency $\omega$ can be expressed using the frequency as $\omega=2\pi f$. This yields a maximum velocity of $v_{max}=2\pi Af$ and will yield an energy of $$E=\frac{1}{2}m(2\pi Af)^2=2m\pi^2 A^2 f^2$$ Substituting known values of $m=1.8kg$, $A=7.1cm=0.071m$, and $f=2.6Hz$ yields an energy of $$E=2(1.8kg)\pi^2(0.071m)^2(2.6Hz)^2=1.2J$$
