Q3. Given the periodic function given by f(t) = 0 - < t < 0 R...
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Q3. Given the periodic function given by f(t) = 0 - < t < 0 R = πt - t 0<t< Solve the following DE (i) A mass of (4+R)kg is suspended to a horizontal spring and is acted upon by the periodic force f(t). The spring constant is (5+R)N/m. Calculate the fourier series of displacement x(t). (ii) An LC circuit of Inductance (2.0+0.1R)× 10-²Henry and Capacitance (8.0 + 0.1)µF. The external AC voltage is given by f(t). Calculate the fourier series of charge in circuit Hints: Step 1: First, express x, q(t) and f(t) as fourier series under different summation index e.g. 1, m on each side Step 2: Combine all the terms on both sides under common E₁g₁(x) = Emhm (x) Step 3: Ensure same range of l and m, i.e, from 0→ ∞o. Then set 1 = m = k Step 4: Equate the coefficients on both sides Q3. Given the periodic function given by f(t) = 0 - < t < 0 R = πt - t 0<t< Solve the following DE (i) A mass of (4+R)kg is suspended to a horizontal spring and is acted upon by the periodic force f(t). The spring constant is (5+R)N/m. Calculate the fourier series of displacement x(t). (ii) An LC circuit of Inductance (2.0+0.1R)× 10-²Henry and Capacitance (8.0 + 0.1)µF. The external AC voltage is given by f(t). Calculate the fourier series of charge in circuit Hints: Step 1: First, express x, q(t) and f(t) as fourier series under different summation index e.g. 1, m on each side Step 2: Combine all the terms on both sides under common E₁g₁(x) = Emhm (x) Step 3: Ensure same range of l and m, i.e, from 0→ ∞o. Then set 1 = m = k Step 4: Equate the coefficients on both sides
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Related Book For
Fundamentals Of Electric Circuits
ISBN: 9780073301150
3rd Edition
Authors: Matthew Sadiku, Charles Alexander
Posted Date:
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