Finding Differential Equation for Circuit: Help Needed!

AI Thread Summary
The discussion focuses on finding the differential equation for a specific circuit, with the user seeking confirmation of their work. A respondent confirms that the user's equation is correct, identifying it as a standard second-order equation representing a damped harmonic oscillator. They explain that without resistors, the circuit would behave as a simple harmonic oscillator, but the resistors introduce damping due to energy dissipation. The user appreciates the feedback received. This exchange highlights the importance of understanding circuit dynamics in differential equations.
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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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!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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