Displacement of Two Waves Oscillating - Mathematics

Internal Code: MAS6944

Mathematics Assignment:

Question 1) The displacement of two waves oscillating together in the same frame perform motions described by the following equations a) Ft= 10cos (4/3t) b) Ft= 10sin (3t) Find the frequency, periodic time and amplitude of the above wave functions and that of their results when they interact by superposition. 2) The displacement of a certain object can be modeled by the sinusoidal function described by 2Cos x + 3 Sin x. Convert it into the form R Sin (x +a), where R > 0 and 0 < a < 90. Find R and x and plot the resultant sine function and also separately plot 2 Cos x and ?3 Sin x. All plots must be on the same paper. Comment on all three graph plots. 3) What is the largest Area of a rectangular field that can be enclosed by a fence of total length 800m? 4) Find the rate of change of the total surface area of a right circular cone at the instant when the base radius is 15cm and the height is 32cm if the radius is increasing at 15mm/s and the height is decreasing at 25mm/s