A mass of 5kg is hung from a tension spring causing an increase in the length...
A mass of 5kg is hung from a tension spring causing an increase in the length of the spring by 18mm. Calculate the following: a) The period of the vibration. b) The frequency of the vibration. c) Determine the maximum velocity and maximum acceleration of the mass when it is pulled down a further 15 mm. d) If a 15 kg machine is suspended from this spring and the machine exerts an out-of-balance force of 10 N at 5 Hz. Determine the amplitude of the steady state vibration.
Homework Answers
Solution
Let xst be the steady state deflection.
FBD when mass spring is loaded and mass is in equilibrium
FBD when mass is is motion
Natural Frequency and Time period
Stiffness of the spring
Maximum velocity and Maximum acceleration
Vibration of system with unbalanced mass
Therefore
the magnitude of amplitude of steady state vibration is 0.828
mm.
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