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e. Using your answers from part d, express ( x, + x2). (2x - 4x2), and ( x, +x2)( 2x1 - 4x2) in a similar forms. Convert this expression into the equivalent forms of R sin(100nbt + a).

e. Using your answers from part d, express ( x, + x2). (2x - 4x2), and ( x, +x2)( 2x1 - 4x2) in a similar forms. Convert this expression into the equivalent forms of R sin(100nbt + a).

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Answer task (4), part (e). The answers to part (d) attached.

Task 4 A support beam 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 equations,x, = 3.75 sin (100nt +) mm X2 = 4.42 sin (100nt -) mm a. State the amplitude, phase, frequency and periodic time of each of these waves. b. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? c. At what time does each vibration first reach a displacement of – 2mm? d. Use the compound angle formulae to expand x, and x, into the form A sin 100nt + B cos 100nt, where A and B are numbers to be found. e. Using your answers from part d, express (x, + x2). ( 2x, - 4x,), and ( x, + x2)( 2x, - 4x,) in a similar forms. Convert this expression into the equivalent forms of R sin(100tbt + a). f. Express the 10th term of ( x, + x,)20 in terms of sinusoidal functions (sin, cos).
Transcribed Image Text:Task 4 A support beam 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 equations,x, = 3.75 sin (100nt +) mm X2 = 4.42 sin (100nt -) mm a. State the amplitude, phase, frequency and periodic time of each of these waves. b. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? c. At what time does each vibration first reach a displacement of – 2mm? d. Use the compound angle formulae to expand x, and x, into the form A sin 100nt + B cos 100nt, where A and B are numbers to be found. e. Using your answers from part d, express (x, + x2). ( 2x, - 4x,), and ( x, + x2)( 2x, - 4x,) in a similar forms. Convert this expression into the equivalent forms of R sin(100tbt + a). f. Express the 10th term of ( x, + x,)20 in terms of sinusoidal functions (sin, cos).
Xit Xz= 1.506 Sinciooit) +(1.789) Costrat +cos 2T 'Sin 2IT 815 (Sin10o0nt Caos 2T +4.42(Sinto0nt cos 2T los'10017t Sin 2 3.15 sinlo0 ntxO.766 + 3. 1S losloont6.6427 Sinloo Tik yD.3090 it yO.3095 - 4.42 coslo0TE(O.951) 2.8725.Sinl0oTIķ + 2.4101 cos100 9t +1.36 Sin Tit_ 4.20 Cos lount = li506 Sin(ITIDOE) + 1.789 asjo0 TIt hene Xit Xq= 1.506 Sinciootit) +(l.789) Costrant 100 cs Scannbia CS CamScanner Scanneieu I506=A & B-1.789
Transcribed Image Text:Xit Xz= 1.506 Sinciooit) +(1.789) Costrat +cos 2T 'Sin 2IT 815 (Sin10o0nt Caos 2T +4.42(Sinto0nt cos 2T los'10017t Sin 2 3.15 sinlo0 ntxO.766 + 3. 1S losloont6.6427 Sinloo Tik yD.3090 it yO.3095 - 4.42 coslo0TE(O.951) 2.8725.Sinl0oTIķ + 2.4101 cos100 9t +1.36 Sin Tit_ 4.20 Cos lount = li506 Sin(ITIDOE) + 1.789 asjo0 TIt hene Xit Xq= 1.506 Sinciootit) +(l.789) Costrant 100 cs Scannbia CS CamScanner Scanneieu I506=A & B-1.789
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