Scenario:
In your role as a Junior Engineer in a local council you are heavily involved in energy management and plant
maintenance. Your line manager has decided to explore the possibility of utilising vibration condition monitoring for
some of the rotating equipment for which they have responsibility.
Activity 1:
Your line manager has asked you to enhance your knowledge of vibrating systems by completing the tasks below. This
will enable you to contribute to a report that’s being prepared to support the case for introducing conditioning
monitoring.
Task 1:
With reference to a mechanical free oscillating mass-spring system.
a) In a short paragraph explain the term ‘simple harmonic motion’.
b) Briefly explain the natural frequency of a system (fn).
c) Explain, using appropriate equations, what properties of the system could be altered to change natural frequency of a system, stating whether these property changes increase or decrease the natural frequency ωn.
Task 2:
A mass of 1.5 kg is attached to a vertical spring, as shown in Figure 1. When the mass is displaced downwards a
distance of 55 mm from its position of rest and released, it is observed to oscillate 60 times in 72 seconds. Determine:
a) the amplitude
b) the periodic time T
c) the stiffness of the spring k
d) the angular velocity ω
e) the time taken to travel upwards a distance of 25 mm for the first time (don’t forget to include the
phase angle due to the starting point).
f) the velocity vc at this point.
g) if damping is introduced into the system, sketch a typical displacement response curve when the
damping ration (ζ) = 1.