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Driven Damped Oscillator
创建日期：2024-04-03 15:48:11
所属分类：物理Physical
标签： ESSMENT
Driven Damped Oscillator

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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

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