![]() Evaluate the solution u ( x, t ) for upto n = 6. Using MATLAB find the solution for u ( x, t ). In Mathematical Calculus, the expanded form of a periodic function f(x) in terms of an infinite sum of cosines & sines is called as Fourier series. Using MATLAB find the solution for u ( x, t ). 3) Find and sketch or graph the deflection u ( x, t ) of a vibrating string of length π, extending from x = 0 to x = 5 π /2 and c 2 = T / ρ = 5 starting with zero velocity and deflection: f ( x ) = 5 e x + x, 0 ≤ x ≤ 5 π /2 a) Assume g ( x ) = 0. Compare the concept with the given problem. ![]() Observe the effect of sampling frequency by assigning different values and comment on it. ![]() The sum of the terms (shown in the top plot) and the actual square wave are shown in the bottom plot. Each term in the Fourier series is shown in the upper plot. Assign sampling frequency as 5000 and modulation index as 0.5. This MATLAB simulation shows how a periodic square wave can be built by summing sine and cosine waves with specific frequencies and amplitudes (Fourier series). 2) Using MATLAB perform amplitude modulation of a wave at 750 Hz frequency. Survey on real life application of Fourier Series. b) Comment on Gibbs phenomena of square wave. ![]() a) using MATLAB, find the first seven Fourier coefficients and plot. 1) Calculate Fourier Series of a square wave with amplitude 8 V within the interval.
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