LC Ocillations given only one piece of data

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In summary, the period of oscillation is 1.61 microseconds and the maximum electric energy is converted to magnetic energy two times during a period. The cosine function has its maximum at t=0 and is equal to zero at T/4. The period can be represented by 2pi and at T=pi/2, the cosine is equal to zero.
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Homework Statement


All the electric energy in a capacitor is converted to magnetic energy in 1.61 micro seconds. What is the period of oscillation?

Homework Equations


I assume Ue = q^2/2c, Ub = -.5 Li^2, w = 1/sqrt(LC) = 2 pi f

The Attempt at a Solution


I worked around the equations Ue = q^2/2c cos^2(w t + phi) and Ub = .5 Lw^2 q^2 sin^2(w t + phi) to get w t = pi/4, but the computer says that 1.288e-5 s is not the answer
 
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  • #2
anyone?
 
  • #3
When the whole energy is in the capacitor, the energy in the inductor is zero, and vice versa. The energy is maximum in the inductor when the electric field is equal to the amplitude or the negative amplitude of E=A sin(wt). The same is true for the magnetic field in the inductor. Sketch the time dependence of both the electric field and the magnetic field. How many times during a period is the maximum electric energy converted to magnetic energy ?
 
  • #4
2 times?
 
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  • #5
No. Draw a cosine function. It has maximum at t=0. When is the cosine equal to zero in terms of the period T?

ehild
 
  • #6
T/4. so.. divide my answer by 4?
 
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  • #7
How does pi come in?

ehild
 
  • #8
if the period is 2pi, then it would be at T = pi/2?

edit: forget it. it was a "N". my mistake
 
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Related to LC Ocillations given only one piece of data

1. What is an LC oscillation?

An LC oscillation is a type of electrical oscillation that occurs in a circuit containing an inductor (L) and a capacitor (C). When the capacitor is charged, it stores energy in the electric field. As the capacitor discharges, the stored energy is transferred to the inductor, which then produces a magnetic field. This cycle repeats, resulting in a continuous oscillation.

2. How is the frequency of an LC oscillation determined?

The frequency of an LC oscillation is determined by the values of the inductor and capacitor in the circuit, as well as the total resistance. It can be calculated using the equation f = 1/(2π√(LC)), where f is frequency, L is inductance, and C is capacitance.

3. What is the role of damping in an LC oscillation?

Damping refers to the reduction of oscillation amplitude over time. In an LC oscillation, damping is caused by resistance in the circuit. Higher resistance results in faster damping, while lower resistance allows the oscillation to continue for longer periods of time.

4. How does changing the inductance or capacitance affect an LC oscillation?

Changing the inductance or capacitance in an LC circuit will alter the frequency of the oscillation. Increasing the inductance will decrease the frequency, while increasing the capacitance will increase the frequency. Additionally, a larger inductance or capacitance will result in a longer oscillation period.

5. What is the significance of only having one piece of data for an LC oscillation?

Having only one piece of data for an LC oscillation is not enough to accurately determine the frequency or other characteristics of the oscillation. Additional data, such as the amplitude or multiple time points, is needed to fully understand and analyze the oscillation. One data point can provide some information, but it is not enough on its own to draw conclusions about the oscillation.

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