A damped harmonic oscillator involves a block (m = 1.91 kg), a spring (k = 12.6 N/m), and a damping force F = −bx˙. Initially, it oscillates with an amplitude of 26.2 cm; because of the damping, the amplitude falls to three-fourths of this initial value after ν = four complete cycles. (a) What is b in terms of the given quantities, and numerically? You may use the approximation that ω1(KK)= ω 0 (RHK4)= p k/m = ω0(KK). (b) How much energy is lost 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 = −bx˙. Initially, it oscillates with an amplitude of 26.2 cm; because of the damping, the amplitude falls to three-fourths of this initial value after ν = four complete cycles. (a) What is b in terms of the given quantities, and numerically? You may use the approximation that ω1(KK)= ω 0 (RHK4)= p k/m = ω0(KK). (b) How much energy is lost during these four cycles?
Vinícius Nunes , 6 Years ago
Grade 12th pass
