Mechanical Engineering
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Theory of machines year 4 engineering question

Question

A steel disc 300 mm diameter of mass 29kg, is suspended from the end of a wire 2.5 mm diameter and 1.5 m long which is clamped into a central hole in the disc. The upper end of the wire being rigidly supported. When the disc is set in torsional vibration, it is found to make 10 complete oscillations in 78.2 seconds.

a) Find the modulus of rigidity of the wire,
b) Calculate the amplitude of the oscillation which may be allowed if the maximum permissible
intensity of shearing stress in the wire is 140 MN/m2

Thanks

2 minutes ago, Temidayodavid said:

A steel disc 300 mm diameter of mass 29kg, is suspended from the end of a wire 2.5 mm diameter and 1.5 m long which is clamped into a central hole in the disc. The upper end of the wire being rigidly supported. When the disc is set in torsional vibration, it is found to make 10 complete oscillations in 78.2 seconds.

a) Find the modulus of rigidity of the wire,
b) Calculate the amplitude of the oscillation which may be allowed if the maximum permissible
intensity of shearing stress in the wire is 140 MN/m2

Thanks

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For starters, the shear modulus is a factor in determining the stiffness which in turn is a factor in determining the undamped natural frequency. Thus you should be able to work back to t he shear modulus from the natural frequency. Give it a try.

DrD

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