Q 1. Given the periodic function given by TU 20 f(t) = 0 Solve the following...

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Q 1. Given the periodic function given by TU 20 f(t) = 0 Solve the following DE < t < 0 Hints: = π-t 0<t<. π 20 (i) A mass of (24)kg is suspended to a horizontal spring and is acted upon by the periodic force f(t). The spring constant is (25)N/m. Calculate the fourier series of displacement x(t). -2 (ii) An LC circuit of Inductance (2.0+0.1(20))x 10 Henry and Capacitance (8.0+ 0.1)µF. The external AC voltage is given by f(t). Calculate the fourier series of charge in circuit Step 1: First, express x, q(t) and f(t) as fourier series under different summation index e.g. I, m on each side Step 2: Combine all the terms on both sides under common Eigi(x) = Emhm (x) Step 3: Ensure same range of I and m, i.e, from 0-→ ∞. Then set 1: = m = k Step 4: Equate the coefficients on both sides. Q 1. Given the periodic function given by TU 20 f(t) = 0 Solve the following DE < t < 0 Hints: = π-t 0<t<. π 20 (i) A mass of (24)kg is suspended to a horizontal spring and is acted upon by the periodic force f(t). The spring constant is (25)N/m. Calculate the fourier series of displacement x(t). -2 (ii) An LC circuit of Inductance (2.0+0.1(20))x 10 Henry and Capacitance (8.0+ 0.1)µF. The external AC voltage is given by f(t). Calculate the fourier series of charge in circuit Step 1: First, express x, q(t) and f(t) as fourier series under different summation index e.g. I, m on each side Step 2: Combine all the terms on both sides under common Eigi(x) = Emhm (x) Step 3: Ensure same range of I and m, i.e, from 0-→ ∞. Then set 1: = m = k Step 4: Equate the coefficients on both sides.

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Solution The differential eqh for given Problem is given by mx Kx Ft Given m 24kg k 25Nm ... View the full answer