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3:49
Convolution is a topic many students find challenging. In this video, I demonstrate the graphical method for solving convolution integrals. Step 1: Graph the two functions/signals Step 2: Change the independent variable from 𝑡 to 𝜏 Step 3: Choose one of the two functions to flip (reflect about the vertical axis) Step 4: Give this reflected signal a horizontal translation/shift of 𝑡 units. Step 5: Investigate the regions of overlap between this transformed signal and the other signal. Set up a
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Control systems exercise: find the percent overshoot of the system with the given transfer function. A second-order system doesn’t always settle smoothly. In many real-world systems, the output temporarily exceeds its final value before settling — a phenomenon known as percent overshoot. Why does this matter? Because overshoot isn’t just a mathematical quantity. In practical applications, excessive overshoot can lead to mechanical stress, voltage spikes, temperature excursions, or reduced passen
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Can you solve this limit problem in one minute? We’ll take a quick look at the engineering method of showing this limit evaluates to e, as well as a more formal mathematical way. #math #calculus #engineering
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Let’s integrate sin(x) / x from 0 to infinity, known as the Dirichlet integral. The integrand, sin(x) / x, is the unnormalized sinc function sinc(x) that is crucial in electrical engineering, particularly in signal processing. In the frequency domain, an ideal “brick-wall” low-pass filter is a rectangular pulse. Taking the inverse Fourier transform of this rectangular pulse gives you a sinc function in the time domain. If you integrate the sinc function up to a variable t (which gives the Sine I
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