 Hello, welcome to yet another demonstration video for the course signals and systems. As we have studied in module 2 about the Eigenfunction property of the LTI system, we know that when a sinusoid input is sent into an LTI system, the output is again a sinusoid, but with a different frequency and phase, so we are going to practically observe this today. So here is the schematic diagram of the apparatus that we are going to use today. It's a simple RC circuit and the output is the voltage observed across the capacitor. The input and the output voltage are related by this equation. We know that the transfer function is the ratio of the output voltage to the input voltage. Hence, we denote it by H of omega. Here H of omega is 1 upon 1 plus j RC omega, which can be further simplified into this form. Now the modulus of H of omega is equal to 1 upon under root 1 plus RC omega square. And the argument of H of omega is given by minus tan inverse RC omega. So here is our apparatus. We have a simple RC circuit with a resistor of 1 kilo ohms and a capacitor of 1 micro ferrats. Here, from here we give the input to the RC circuit and through these probes we fetch the output on the digital oscilloscope. As we have a resistor of 1 kilo ohm and capacitor of 1 micro ferrat, then the transfer function equations can be simplified as follows. The transfer function can be written as 1 upon 1 plus j 10 to the power minus 3 omega or it can be further written as 1 minus j 10 to the power minus 3 omega whole upon 1 plus 10 to the power minus 3 omega square. Hence, the amplitude of the transfer function can be written as 1 upon under root 1 plus 10 to the power minus 3 omega whole squared and the argument of the transfer function can be written as minus tan inverse 10 to the power minus 3 omega. First, we will send a sinusoid of frequency 500 hertz as an input to the RC circuit. So if the frequency is 500 hertz, the angular frequency omega 1 is equal to 1000 pi radians per second or 3141.59 radians per second roughly. This implies that the transfer function h omega 1 is equal to 1 upon 1 plus j pi and the amplitude of the transfer function is 0.303 roughly and the argument is equal to minus 1.2626 to 7 radians. Here on the oscilloscope, we will see the waveform with the larger amplitude as the input and the waveform with the smaller amplitude is the output. The ratio of the two amplitudes turns out to be 0.3. Now you will also see the phase shift between the input and the output. To find the phase difference, we have to calculate the time difference between the two peaks and multiply it with the angular frequency. In this case, it is 1000 pi radians per second. Now for omega equal to 1000 pi radians per second, we have calculated the amplitude of the transfer function to be 0.303 and the argument of the transfer function to be minus 1.2627 radians. From the practical observation, we get that the amplitude of the transfer function is 0.3 roughly and the argument of the transfer function is minus 1.162 radians which is under the experimental error. Similarly, for the sinusoidal frequency 2000 hertz or 2 kilohertz, we can find out the angular frequency to be 4000 pi radians per second and through this we can find out the amplitude of the transfer function to be 0.079 and the argument of the transfer function to be 1.4914 radians. Here again you can see the input waveform with the larger amplitude and the output waveform with the smaller amplitude and the ratio of the amplitude of the output waveform to the input waveform comes out to be roughly 0.081. Through the practical observations, we have found out that the amplitude of the transfer function is 0.081 and the argument turns out to be minus 1.3823 radians. We have found the argument in the same way as we did for the previous frequency and we have carefully take the values which for the amplitude of the transfer function which comes out to be 0.079 and the argument comes out to be minus 1.4914 radians. This is Jatant Ursham signing off from the demonstration video. We will be seeing each other again very soon. Thank you.