How Can Engineering Concepts Solve the Two Pulleys Problem?

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Homework Statement



I am having trouble completing these questions, help would be much appreciated.

thanks

Lukas

Homework Equations





The Attempt at a Solution

 
Attachments
  • Engineering diagram of a gear train on a shaft, labelled with teeth counts t4 = 64, t5 = 96, t3 = 48, wheels numbered 1 to 4 and 5, marked NOT TO SCALE, with axis X1 at right.
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  • Diagram of a quarter-car suspension model: a mass m on springs k/2 and a damper c above a wheel, driving over a sinusoidal road profile with height Y, horizontal axis x, wavelength L and travel direction V.
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  • Dynamics assignment sheet showing a mass m suspended from a pulley system with springs labelled k, 2k and 5k, pulleys of radius r and 2r, displacement x(t), and two text questions (a) and (b) with marks.
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Welcome to PF!

Hi Lukas! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
I have attached my partial solution to the two pulleys question. I think I have managed to work out the natural frequency, however I don't know what to do more as there are different spring stiffnesses and the pulleys have different radii.
 
Attachments
  • Handwritten derivation on lined paper for a two-pulley oscillation problem: torsional inertia force T = I alpha, spring force F = kx, sum F = ma + kx + alpha/r, and free-oscillation result omega = sqrt(k/(r^2 m)), natural frequency f = (1/2pi) sqrt(k/(r^2 m)).
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Lukas Pohnan said:
I have attached my partial solution to the two pulleys question. I think I have managed to work out the natural frequency, however I don't know what to do more as there are different spring stiffnesses and the pulleys have different radii.

Hi Lukas! :smile:

Sorry, but this is too difficult to read.

Can you please type out your work in future?

(btw, there's no torsion in the pulley question)