Many tall building have mass dampers, which are antisway devices to prevent them from oscillating in a wind. The device might be a block oscillating at the end of a spring and on a lubricated track. If the building sways, say eastward, the block also moves eastward but delayed enough so that when it finally moves, the building is then moving back westward. Thus, the motion of the oscillator is out of step with the motion of the building. Suppose the block has mass `m= 2.72 xx 10^(5)kg` and is designed to oscillate at frequency f= 10.0 Hz and with amplitude `x_(m) = 20.0cm`.
What is the total mechanical energy E of the spring block system?

Explanation

To find the total mechanical energy \( E \) of the spring-block system in simple harmonic motion (SHM), we can use the formula for the total mechanical energy:

\[ E = \frac{1}{2} m \omega^2 A^2 \]

where:
- \( m \) is the mass of the block,
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