A support beam used in one of the designs for the theme park, 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 attached equations:   For the attached equations you are required to determine the followings for the vibration of this beam: 1-At what time does each vibration first reach a displacement of −2??? 2- Use the compound angle formulae to expand and into the form   ? sin 100??  ? cos 100??, where ? and ? are numbers to be found. 3-Using your answers from part 2, express in a similar form. Convert this expression into the equivalent form ? sin (100?? +

The figure below (for illustrative purposes) shows a perfectly rigid (non-deformable) beam which is perfectly rigidly supported at points P and R by two force measurement scales, 1 and 2. PQ is 65 cm and PR is 150 cm. The beam is horizontal when each of scales 1 and 2 gives a reading of zero. Acceleration due to gravity is 9.81 ms-2. Scale 1 Point P Point Q Point R Scale 2 Choose one of the following options that will give the correct readings of scales 1 and 2 when a mass of 30 kg acts vertically downwards at point Q. (The scales are not loaded to you will have to calculate the answer) O A Reading of Scale 1 = 150 kg; Reading of scale 2 = 65 kg O B. Reading of Scale 1 = 166.77 kg; Reading of scale 2 = 127.53 kg O C. Reading of Scale 1 = 150 Newton; Reading of scale 2 = 65 kg O D. Reading of Scale 1 = 166.77 Newton; Reading of scale 2 = 127.53 Newton

Question 1b

use this matrix num sir (ad 200107)