Rise And Fall Of The Clockwork Universe

Question 1

How do you create an iterative model for the discharge of a capacitor?

Answer 1

1. Rearrange ΔQ/Δt = -Q/RC for ΔQ
2. Find the new Q by doing Q_old - ΔQ
3. Repeat for as many iterations as necessary

Question 2

Define the decay constant (λ)

Answer 2

The probability that a nucleus will decay in the next unit of time

Question 3

Why does a smaller Δt lead to a better decay model?

Answer 3

1. The assumption that decay is constant over Δt becomes more accurate
2. When plotted on a graph, the curve is smoother and better reflects the exponential nature of decay

Question 4

How do you calculate energy stored in a capacitor?

Answer 4

E = 1/2 * Q * V = 1/2 * C * V² = 1/2 * Q²/C

Question 5

How does resonance occur?

Answer 5

When driving frequency is equal to natural frequency

Question 6

What happens to the resonance peak as a system is dampened more on a graph of amplitude against natural frequency?

Answer 6

It becomes shorter, wider and shifts to the left.