Question
A circuit with $R=1, L=2, C=4$, includes an alternating current source $F(t)=25 \cos 2 t$. Find the solution to the initial value problem $u(0)=1, \dot{u}(0)=0$.
Step 1
The differential equation for an RLC circuit with resistance \( R \), inductance \( L \), and capacitance \( C \) driven by a voltage source \( F(t) \) is given by: \[ L \frac{d^2 u}{dt^2} + R \frac{du}{dt} + \frac{1}{C} u = F(t) \] Plugging in the given values \( Show more…
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