RLC ckt's underdamped response

In summary, the underdamped response of an RLC circuit is when the current and voltage oscillate around a steady-state value, with the amplitude of the oscillations decreasing over time. This is different from the overdamped response, where there are no oscillations due to a high damping factor. The underdamped response is affected by the values of resistance, inductance, and capacitance, and can be analyzed mathematically using the equation for the current in an RLC circuit. Understanding this response is important for designing and analyzing circuits in fields such as electronics and electrical engineering.
  • #1
barneygumble742
28
0
hi...

how can i get A cos (omega t) + B sin (omega t)

into this form: C cos (omega t + theta) ?

does it equal to A+B cos (omega t - 90) ?

i know it has to do with the underdamped response of an RLC circuit. i
was looking into phasors as well.

any help would be greatly appreciated.

mark
 
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  • #2
I do not think you can friend.
 
  • #3
If A=B and C=2A, I think you can get it to work. But not in the general case where the amplitudes of the sin and cos components are different.
 

1. What is RLC circuit's underdamped response?

The underdamped response of an RLC circuit refers to the behavior of the circuit when it is excited by a step input. In this response, the current and voltage in the circuit oscillate around a steady-state value, with the amplitude of the oscillations decreasing over time.

2. How is the underdamped response different from the overdamped response?

The overdamped response of an RLC circuit occurs when the damping factor is high enough to prevent any oscillations in the current and voltage. This results in a slower rise time and longer settling time compared to the underdamped response.

3. What factors affect the underdamped response of an RLC circuit?

The underdamped response is affected by the values of resistance, inductance, and capacitance in the circuit. A higher resistance will result in a faster decay of the oscillations, while a higher inductance or capacitance will cause the oscillations to last longer.

4. How can the underdamped response of an RLC circuit be analyzed mathematically?

The underdamped response can be analyzed using the equation for the current in an RLC circuit, which takes into account the values of resistance, inductance, and capacitance, as well as the initial conditions. This equation can be solved using techniques such as Laplace transforms or differential equations.

5. What practical applications does understanding the underdamped response of an RLC circuit have?

Understanding the underdamped response of an RLC circuit is important in fields such as electronics and electrical engineering. It can be used to analyze and design circuits for various applications, such as filters, oscillators, and amplifiers.

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