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

At ` x= x_(m), `velocity `= v=0`
`k= m omega^(2)= m(2 piv)^(2)`
`= ( 5.44 xx 10^(5)kg) ( 2pi)^(2) ( 5 sqrt(2) Hz)^(2)`
`=1.073 xx 10^(9) N//m`
Total mechanical energy `, E= K +U`
`(1)/(2) mv^(2) +(1)/(2) kx^(2)`
`= 0 + (1)/(2) xx 1.073 xx 10^(9) N //m xx( -.40 m)^(2)`
` = 8.588 xx 10&(7) J = 8.6 xx 10^(7) J`