Many builidings have other types of mass dampersas antisway devices ( Refers of Example 14) some like the Johns Honacock building in Boston,have a larger block oscillating at the end of spring and an a lubricated track. .Suppose the block has `m=5.44 xx 10^(5) kg` and is designed to oscillate at a frequency of`5 sqrt(2)` Hz and with amplitude ` x_(m) = 0.40 m` . Find the total mechanical energy E of the spring block system.
Hint `:K =m omega^(2) = m ( 2pi v ) ^(2)`
`E = K+U = (1)/(2) mv^(2) + (1)/(2) kx^(2)`

Explanation

To find the total mechanical energy \( E \) of the spring-block system, we can use the formula for total energy in a harmonic oscillator, which is given by:

\[ E = K + U = \frac{1}{2} mv^2 + \frac{1}{2} kx^2 \]

Where:
- \( K \) is the kinetic energy,
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