The logarithmic decrement ? of a lightly damped oscillator is defined to be the

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The logarithmic decrement ? of a lightly damped oscillator is defined to be the natural logarithm of the ratio of successive maximum displacements (in the same direction) of a free damped oscillator. That is, ? = ln(A_n/A_(n+1)) where A_n is the maximum displacement of the nth cycle. Derive the simple relationship between ? and Q. FInd the spring constant k and damping constant b of a damped oscillator with mass m, frequency of oscillation f and logarithmic decrement ?. [Data: m = 4.8 kg; f = 0.5 Hz; ? = 0.030.] (a) Find the spring constant k.... (b) Find the damping constant b....

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