Finding the differential equation for a circuit

[ur5pointos2sl]

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.

 

[cepheid]

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.

 

[ur5pointos2sl]

Thank you!