Differential equation based on Kirchoff's voltage law

[asdf1]

a series circuit with an inductance of 15mH, a capacitance of 35*10^(-6) F and a resistance of 5 ohms conatain a sinusoidal source of emf with a frequency of 500Hz. The frequency with which the charge on the capacitor oscillates is?

i think that it should still be 500Hz, right?

 

[mezarashi]

Yes, you are right. This can be verified by writing out the differential equation based on Kirchoff's voltage law and solving for the current or voltage across the capacitor.

These are known as forced oscillations. Suppose you have a physical spring. If you hang a mass on it and perturb it, it will oscillate at some natural frequency. You can also of course, hold onto the mass with your hand and make it move at any frequency you desire.

Additional note: You also must assume steady state conditions. In transients you will find that there will be the forced + natural responses to a system.

 

[asdf1]

thank you very much!