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程序代写案例-ESSMENT 1

时间：2021-03-01

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

学霸联盟

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

学霸联盟