First pic is backgrownd info! Pls help! Thanks!!!! Asimple harmonic oscillator e

Question

First pic is backgrownd info! Pls help! Thanks!!!!

Asimple harmonic oscillator exhibits sinusoidal behavior. As you saw in tutorial, the charge on the capacitor and the current through the inductor in an LC circuit oscillate sinusoidal in time, so an LC circuit is a simple harmonic oscillator. inductance, represented with the symbol Lis a measure of how strongly an inductor opposes a change current. Question 1: Consider an LC circuit with an initial charge Qo, inductance Lo and C L capacitance Co. In tutorial, you found that the charge on the capacitor Qt) varied in time as shown in the plot at right. The general expression for a sinusoidal curve that begins at a ,o maximum is given by Acos where A is the amplitude and is the angular frequency. Suppose the inductance were doubled to 2Lo.

Explanation / Answer

1) less quickly

2) Applying KVL equations

We get

d^2I(t)/dt^2 + (1/LC) I(t) = 0

So change in current will be slower

4) w = 1/sqrt(LC)

So less than due to inverse relationship

3) t = 2pi/w

Hence it increases

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