Question

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,

x120sin(at+ i. ii. iii. State the amplitude, phase, frequency and periodic time of each of these waves Add and subtract the given waveforms using phasor method. Use the COmpoundangleformulac to expand x1 and x2 into the form A sin wt ± B cos wt, where A and B are numbers to be found. Express (x1 + x2) into the form A sin wt ± B cos wt. Convert this expression into the equivalent form R sin (wt + α) Using appropriate spread sheet software, copy and complete table 1 v. Table 1: Addition and subtraction of sinusoidal waves 0 45 90 135 180 225 270 315 360 (xl+x2) (xl-x2) vi. Plotxl, x2, (xl +x2), (xl - x2) on the same graph sheet and also using any suitable computer package. Find amplitude and f frequency of the new waves. vii Compare phasor and graphical method of addition and subtraction by using results from task (ii) and task (vi).

Answer 1

3 For hirst wave For 2 woe Ampli-tudle 3 Phare 中2. 3 eduen 2 11 Time Period 24 Addition 아.tuowave入 Ay 2. ㄚ lo A2 Y . 24-56

Substractron A2 2-3 = 135-60 :750 2 A12 2 : 180-cm

iv = (けん 4 3. 14-2. Sinu)トレ//i 2.8 o \\ (cchut 3.1411+ 21-80 V9.141 12-30