A simple RC-circuit with emf V(t) = 3 cos (ωt) is modeled by the initial value problemwher...

A simple RC-circuit with emf V(t) = 3 cos (ωt) is modeled by the initial value problem

where R is the resistance, C the capacitance, ω is the driving frequency, and VC is the voltage response across the capacitor. Show that the solution is

Create a function M-file for this solution as follows

Now, call this function with the following script.

Run this script for ω = 1,2,4, and 8, keeping R = 1.2 ohms and C = 1 farad constant. What happens to the amplitude of the voltage response across the capacitor as the frequency of the emf is increased? Why do you think this circuit is called a low pass filter?