AIN SHAMS UNIVERSITY FACULTY OF ENGINEERING Design & Production Engineering Department MECHANICAL ENGINEERING PROGRAMS Fall 2022 Assignment -1 [10 marks] Mechanical Vibrations – MDP311 Question 1 [2 marks] For each of the following periodic functions, determine the frequency and then plot the function and each component over two cycles using MATLAB (three plots on one page). b) x = 4 cos 25t + 3 sin 50t, where x is mms and t is in seconds. Question 2 [3 marks] Determine the harmonic analysis (Fourier analysis) of each of the periodic functions shown in Fig. 1. Draw different approximations using different values of the from the Fourier series (n=1, n=1:5, n=1:9) (three different plots) using MATLAB (three plots on one page). Question 3 [5 marks] The crate, of mass 250 kg, hanging from a helicopter shown in the figure can be modeled as shown. The rotor blades of the helicopter rotate at 300 rpm. Find the diameter of the steel cables so that the natural frequency of vibration of the crate is at least twice the frequency of the rotor blades. Consider that the helicopter is stopped (as fixation). Consider the modulus of elasticity is 20 × 1010 𝑁/𝑚2 .
