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Task 3 a) The instantaneous value of voltage in an A.C. circuit at any time t (seconds) is given by: v = 340 sin (son: o. 541) Volts Determine the: (i) Amplitude, frequency, periodic time and phase shift (giving your answer in degrees). (ii) Value of the voltage when t = 0. (iii) Value of the voltage when t =10ms. (iv) Time when the voltage rst reaches 200. (v) Time when the voltage rst reaches a maximum. (vi) Sketch one cycle of the waveform showing relevant points. b) A support beam, within an industrial building. is subjected to vibrations along its length, emanating from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following two equations: Unit 8 Assignment 1 of4 2021-2022 5 x1 = E sin (100m + 11;) 2 x2 = 55111000111 g) (i) Use the compound angle formulae to expand x1 and x2 Into the form A sin(1001'rt) i B cos(1l}0n't) where A and B are numbers to be found. (ii) Using your answer from part (ii), express x1 + x; in a similarform. Convert this expression into the equivalent form R sin(100n't + a) where R and a: are numbers to be determined. Note that you are required to use an appropriate argument so that a satises 0"