A damped harmonic oscillator involves a block (m = 1.91 kg), a spring (k = 12.6 N/m), and a damping force F=-yu. Initially, it oscillates with an amplitude of A = 26.2 cm; because of the damping, the amplitude falls to three-fourths of this initial value after four complete cycles. (1) What is the value of ? (2) How much mechanical energy has been lost by the oscillator during these four cycles.

A damped harmonic oscillator involves a block (m = 1.91 kg), a spring (k = 12.6 N/m), and a damping force F=-yu. Initially, it oscillates with an amplitude of A = 26.2 cm; because of the damping, the amplitude falls to three-fourths of this initial value after four complete cycles. (1) What is the value of ? (2) How much mechanical energy has been lost by the oscillator during these four cycles.