Finding Differential Equation for Circuit: Help Needed!

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SUMMARY

The discussion centers on deriving the differential equation for a circuit that represents a damped harmonic oscillator. The participants confirm that the standard second-order equation is correct, highlighting that the presence of resistors introduces damping to the system. Without resistors, the circuit would behave as a simple harmonic oscillator, where energy oscillates between inductive and capacitive components. The insights provided clarify the role of resistors in energy dissipation within the circuit.

PREREQUISITES
  • Understanding of differential equations in electrical circuits
  • Knowledge of circuit components: resistors, inductors, and capacitors
  • Familiarity with the concept of damped harmonic oscillators
  • Basic circuit analysis techniques
NEXT STEPS
  • Study the derivation of second-order differential equations in electrical circuits
  • Learn about the behavior of damped harmonic oscillators in various systems
  • Explore energy dissipation in resistive circuits
  • Investigate the impact of varying resistance on circuit behavior
USEFUL FOR

Electrical engineers, circuit designers, and students studying circuit theory who seek to understand the dynamics of damped harmonic oscillators in electrical circuits.

ur5pointos2sl
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Hi

I need to try and find the differential equation representing the attached circuit. My work is also being shown on the attachment. Can anyone confirm whether this is correct? If it is wrong could you please provide input as to why? Thanks.

Sorry for the quality in advance.
 

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    Circuit.png
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ur5pointos2sl said:
Hi

I need to try and find the differential equation representing the attached circuit. My work is also being shown on the attachment. Can anyone confirm whether this is correct? If it is wrong could you please provide input as to why? Thanks.

Sorry for the quality in advance.

That's looks fine to me. You get the standard second order equation. It's a damped harmonic oscillator. Without the resistors, it would just be a simple harmonic oscillator, as energy would be transferred back and forth between the ideal inductive and capacitive elements. The resistors add damping because energy is dissipated in them.
 
Thank you!
 

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