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13 Nov 2019
3. Linear Oscillator with Periodic Forcing s0) Consider the second-order differen- tial equation, y" + 4y = f(t) where f(t) is the periodic triangle wave shown in the figure. -2Ï -1 (a) Verify that the Fourier trigonometric series forfhas the form f(t) = Σ b2k-1 sin((2k-I )I). (Calculate the trigonometric Fourier series on the Determine the coefficients b2k fundamental period [-Ï, Ï (b) Find a series representation for a particular solution to the nonhomogeneous ODE y" + 4y = f(t), by finding a particular solution for each term. in the Fourier series for f(t) and then summing these results to get a (formal) solution for ypt)
3. Linear Oscillator with Periodic Forcing s0) Consider the second-order differen- tial equation, y" + 4y = f(t) where f(t) is the periodic triangle wave shown in the figure. -2Ï -1 (a) Verify that the Fourier trigonometric series forfhas the form f(t) = Σ b2k-1 sin((2k-I )I). (Calculate the trigonometric Fourier series on the Determine the coefficients b2k fundamental period [-Ï, Ï (b) Find a series representation for a particular solution to the nonhomogeneous ODE y" + 4y = f(t), by finding a particular solution for each term. in the Fourier series for f(t) and then summing these results to get a (formal) solution for ypt)
Nestor RutherfordLv2
22 Mar 2019