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Math · Advanced Math
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Question 2 19 marks Consider the function 0, -π < t < 0, (2T) f(t). (a) State the fundamental period, and sketch the function over the interval 5) (b) Show that the exponential Fourier series for this functio is | _ (inTT + 1)(-1)) eint n40 where the notation on the summation sign indicates that we sum n over all the integers except zero 17] (Hini: You may find the following standard integral useal: (c) A particle with position a:(0) unde goes driven and damped harmonic motion, aud is described by tlhe differential equation where α is a positive constant, and the periodic driving terni f(t) is given by equation (1). Find the Fourier series for a particular solution of this motion. Describe the nature of the motion as the damping a gets smaller and sillaller (α-+ 0), alld in particular state which angular frequency will dominate the motion. 17] page 2 of 4

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