(2) a) An RLC circuit has the following differential equation (DE) for t > 0. d’v(t)/dt...
Extra Credit: You have an undriven series RLC circuit in which the capacitor was given some initial charge at t=0. a. What is the natural frequency of the circuit in terms of R, L, and C? (2 pts) b. For what R value(s) will the circuit oscillate at the natural frequency? For other R values, will it oscillate at a higher or lower frequency? (2 pts) c. If we call the value of R that causes critical damping Re, then...
5. Extra Credit: You have an undriven series RLC circuit in which the capacitor was given some initial charge at t=0. a. What is the natural frequency of the circuit in terms of R, L, and C? (2 pts) b. For what R value(s) will the circuit oscillate at the natural frequency? For other R values, will it oscillate at a higher or lower frequency? (2 pts) c. If we call the value of R that causes critical damping Re,...
Solve the Next second order system Draw the electric circuit and assign the RLC values with the differential equation data. Solve with the natural and forzed answer. u(t)-''(t) + 7' (t) + 12i(t) i(0) = 2 (t)- 5 v(t)1.5e u(t)-''(t) + 7' (t) + 12i(t) i(0) = 2 (t)- 5 v(t)1.5e
0 in the series RLC circuit shown in Figure 2 switches 51 and 52 both open at t -0. Solve the differential equation for loop current I (t) when the res has a value of 1 Ohm. Be sure to show all work and specify values for alpha, WO, W d, S1, S2, (o), V(o), etc. if they are required for the solution (e.g. s1 and s2 are only needed for an overdamped solution. (300 pts a: - Wo =...
7. Design an Op Amp circuit that solves the following first order differential equation for v(t): dv dt 8. Design an Op Amp circuit that solves the following second order differential equations for y(t): 습+10 y(t) = cos(21t) · dt?
2-a)-RLC components connected in series in a circuit supplied by a variable dc voltage can be described by the following differential equations: di(t) wherei@ is the loop current and V1(t) İs the voltage drop across the inductor.+' The voltage drop across the resistor is given by Ohm's law vR(t) R i(t) and the voltage drop across the capacitor vc(t) is given by i(t) dt For a series circuit ye)t vit)t velt) v(t) where v(t) is applied voltage: Figure 3: RLC...
suppose an input voltage is given as V(t) = 240[u(t-5) - u(t-10)]. In a branch of an electronic circuit, the variation of current with time is modeled by the differential equation d^2(i)/dt^2 + 36i = dv/dt. Assuming zero initial conditions, determine I as a function of t. (hint: use laplace transforms)
A certain physical system is described by the 2nd-order ordinary differential equation +6-0. dt (a) Determine the natural frequency, a, of the system (b) Determine the damping ratio, , of the system. (c) Classify the system as undamped, underdamped, critically damped or overdamped.
dx dt 1. For the circuit below determine: a) The initial conditions: iz(0+), dix(0*), v(0+), dv(0+) b) The circuit differential equation and solve for iz(t), t 2 0 (No credit for Transform techniques) ix VI 102 422 + lo 5+10u(t) 10 H 1/4 F V
3. (40 pts total) Eigenvalues of Systems of Equations Application: Series RLC Circuit, Natural, or Transient Response (Remember EE280, maybe not) M SR v(t) Consider a series RLC circuit, with a resistor R, inductor L, and capacitor C in series. The same current i(t) flows through R, L, and C. The switch S1 is initially closed and S2 is initially open allowing the circuit to fully charge. At t=0 the switch S1 opens and S2 closes as shown above. Solving...