Consider the following circuit equation: I = dV/dt, where V(t) is a potential difference applied to the circuit that varies with time t. Answer the...

Consider the following circuit equation: I = dV/dt, where V(t) is a potential difference applied to the circuit that varies with time t. Answer the following questions: (a) Is this the equation of a harmonic oscillator, damped, forced...? (b) Identify the constant ω0 (natural angular frequency). (c) Identify the constant b. (d) Identify the constant γ. (e) What can be said about the electric current? (f) What electronic component plays the role of "inertia"? (g) What electronic component plays the role of "restoring force"? (h) What electronic component plays the role of "dissipative force"? (i) Which element of the equation above plays the role of "external force"? (j) Suppose L = 0.3 × 10^-6 [the unit is the "Henry" (H), but don't worry about it here]. What should be the value of C for this circuit to oscillate at the same frequency as Radio Rock, at 89.1 MHz? (k) Now suppose that V = 0 (there is no "external force") and that at t = 0 the current has some value I0. What should you do in the circuit to obtain a current that oscillates harmonically, without ever ceasing?
(a) Is this the equation of a harmonic oscillator, damped, forced...?
(b) Identify the constant ω0 (natural angular frequency).
(c) Identify the constant b.
(d) Identify the constant γ.
(e) What can be said about the electric current?
(f) What electronic component plays the role of "inertia"?
(g) What electronic component plays the role of "restoring force"?
(h) What electronic component plays the role of "dissipative force"?
(i) Which element of the equation above plays the role of "external force"?
(j) Suppose L = 0.3 × 10^-6 [the unit is the "Henry" (H), but don't worry about it here]. What should be the value of C for this circuit to oscillate at the same frequency as Radio Rock, at 89.1 MHz?
(k) Now suppose that V = 0 (there is no "external force") and that at t = 0 the current has some value I0. What should you do in the circuit to obtain a current that oscillates harmonically, without ever ceasing?
Exercício 1 Ops! Que tal discutir com seus colegas?
Exercício 2 Veja a resposta do exercício 1.
Exercício 3 O sistema apresenta amortecimento subcrítico. b ≈ 16,64 kg/s.
Exercício 4 (a) 0,39 Hz, (b) b ≈ 1,73 kg/s.
Exercício 5 b ≈ 0,02 kg/s.
Exercício 6 θ̈ +γθ̇ +ω2 0θ = 0, com γ = b /I eω2 0 = K /I , onde K é o “módulo de torção” (análogo à “constante elástica”) e I é o momento de inércial do objeto que oscila.
Exercício 7 (a) x (0) = A; (b) Velocidade de módulo γA/2 e sentido oposto à orientação do deslocamento; (c) A inclinação do gráfico de x (t ) em t = 0 é negativa; (d) ẍ (0) = A1/2γ2−ω20; (e) ẍ (0)< 0 se b < √2k/m, ẍ (0) = 0 se b = √2k/m e ẍ (0)> 0 se b > √2k/m.
Exercício 8 Veja a resposta do exercício 1.
Exercício 9 Veja a resposta do exercício 1.
Exercício 10 (a) A ≈ 1,57 m e B ≈ −0,70 rad; (b) C = 1,2 m e D ≈ 1,01 m; (c) Veja a resposta do exercício 1.
Exercício 11 x (0) = 3, ẋ (0) =−1 e b = 5 kg/s.
Exercício 12 x (t )≈ 0,25e −t sen(19,97t )
Exercício 13 Veja a resposta do exercício 1.
Exercício 14 Veja a resposta do exercício 1.
Exercício 15 Veja a resposta do exercício 1.
Exercício 16 (a)A2 =A1/3 eA3 = 2A1; (b)A4 = 5F0/k eA5 = 2,5F0/k .
Exercício 17 O dispositivo não satisfaz a exigência.
Exercício 18 Veja a resposta do exercício 1.
Exercício 19 (a) Oscilador amortecido e forçado; (b)ω0 = 1/(LC); (c) b = R; (d) γ = R/L; (e) A corrente oscila; (f) O indutor; (g) O capacitor; (h) O resistor; (i) dV/dt; (j) C ≈ 11×10^-12 F (não se preocupe com a unidade); (k) Veja a resposta do exercício 1.