ASSESSMENT 1 : Driven Damped Oscillator Instructions : 1. Complete the assignment question as given below 2. Name your files using the format : “A1_0123456.ipynb” where A1 represents “assignment no. 1” and 0123456 represents the 7 numeric digits in your GUID. 3. Electronic submission – Upload you files to the ENG2083 course Moodle site before 1st March Driven Damped Oscillator : Consider the simplified description of a suspension system as a simple driven damped oscillator (shown in figure 1 below). If the driving force is given by , for example by a series of speed bumps, the equation of motion for the mass is given by : 2 2 + + = The solution of which is given by : = sin ( ) where, F is the amplitude of the driving force ω, the angular frequency b, related to the damping co-efficient k, related to the restoring force m, the mass of the driven object ωo, the natural frequency of the oscillator, and = √2(2 0 2)2 + 22 Write a program to calculate the amplitude of the oscillation (F/G) versus frequency (ω) and plots a series of curves for the following conditions: F m Figure 1 F = specified by user in N ωo = specified by user in rad/s ω = a range specified by the user (start, end, increment) b = 0.25*mω0, 0.50* mω0, 0.75* mω0, 1.00* mω0. Your program should : Ask the user to input the values of F, m, and ωo Ask for the minimum, maximum and increment values for ω. Test to make sure these are sensible limits, i.e. that ωmin ≥ 0, ωmin < ωo < ωmax, and that ωinc < ωmax - ωmin For each of the four values of b, your program should plot the results on a single graph. The figure should be given appropriate axes, title and annotations as required. Find and report the maximum point for each curve i.e. using the array of amplitude values (F/G), find the maximum value and the frequency at which it occurs. Use your program to create a graph with ωo = 1 rad/s, over a frequency range of 0.01 to 5 rad/s with an increment of 0.01 rad/s. A sample figure screen : A sample output window : Amplitude of driving force (N) F = 10 Mass of oscillator (kg) m = 5 Mass of natural frequency (Hz) wo = 1 Please enter the minimum value, maximum value and increment for the frequency, w ... Minimum w value (>0): .001 Maximum w value (> min value): 5 Step increment for the w axis : .02 When b = 0.25*m*wo, max = 8.061 at freq = 0.981 Hz When b = 0.50*m*wo, max = 4.130 at freq = 0.941 Hz When b = 0.75*m*wo, max = 2.876 at freq = 0.841 Hz When b = 1.00*m*wo, max = 2.309 at freq = 0.701 Hz
