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The time constant is defined as the time for the energy of the system to lose 63% of its initial energy. Determine the time constant for the system. Express the following amplitude ratios in terms of period T: ln(A_0/A_1 ),1/2 ln(A_0/A_2 ),〖1/3 ln〗(A_0/A_3 ),〖 1/n ln〗(A_0/A_n ) where A_n is the amplitude after n cycles. Determine values for the damping coefficient and damping constant that will rapidly reduce the oscillations of this system. How much does the damping change the angular frequency? You may wish to use the following: √(1+y)=1+1/2 y-1/8 y^2+1/16 y^3-..
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