Question

A damped harmonic oscillator consists of a block (m = 3.00 kg), a spring (k = 11.1 N/m), and a damping force (F = -bv). Initially, it oscillates with an amplitude of 28.7 cm; because of the damping, the amplitude falls to 0.760 of the initial value at the completion of 6 oscillations. (a) What is the value of b? (Hint: Assume that b² << km.) (b) How much energy has been lost during these 6 oscillations?

Answer 1

(a) A = As cont where da E = GT 3 A= 0.760 A and T20F = 20/ 3.279 t= 6T = 19.68 - 19.64 - 0.014 0.760 = c + 1 = 0.014 st va b= Dosy kole E = F to e 246 è - 2x 0.014х 19.6 e = E = 0.578 to Elost = tort = 0422€ and to = 1 k ² = 1 x (11.1 NM) (0.287m) 2 I to = 0.4575 That 0-1935