- #1

RoyalFlush100

- 56

- 2

**I bolded the portions I need help with.**

1. Homework Statement

1. Homework Statement

A series circuit consists of a resistor with a resistance of 16 ohms, an inductor with inductance of 2 H, and a capacitor with a capacitance of 0.02 F.

At time t = 0 there is no charge on the capacitor and no current in the circuit. If a 9 V battery is connected at at t=0 and disconnected at t=2

(a) The charge, q(t), on the capacitor at all t

**(b) Compute the impulse response of the circuit as a function of time and classify the response as under-damped, over-damped, or critically-damped, explaining your rationale.**

(c) Suppose the resistor were changed to make the circuit response critically-damped. What would be the value of R? Compute the new impulse response with this value B.

(c) Suppose the resistor were changed to make the circuit response critically-damped. What would be the value of R? Compute the new impulse response with this value B.

## Homework Equations

The equation:

2q'' + 16q + 50 = 9(1 - U(t-2)). Where U is the unit step function.

## The Attempt at a Solution

So, I found the q(t) by applying the Laplace Transform on the equation and then the inverse Laplace Transform Q(s). My work for the first part is in the image attached.

However, I am unsure how to calculate the Impulse Response without delta involved in the equation. I believe the circuit is under-damped because: sqrt(16^2 - 4(2)(50)) is not a real solution. However, I don't know how that would relate to the Impulse Response.