Radar system is modelled as a single degree of
freedom with mass 20kg and spring stiffness 75000 N/m. Ignore the effect of damping. The
rotating part of the RADAR imparts a force of 1000sin(ωt) and is designed to rotate at three
different speeds: 5Hz, 10Hz and 15 Hz.
The tender is by open competition, which will be judged not only on the amount of vibration
reduction in the radar system, but also on the minimum increase in mass and the cost of the
The cost of each extra kg is $1 and the cost of each 1000N/m is $1. In order not to interfere with
the supporting structure the minimum resulting natural frequency allowed is 2Hz.
You are asked to submit your tender proposal, including the following:
• Explanation of the theory used
• The design of the absorber where only the reduction in vibration level is considered
• The design of an absorber where vibration level increases in mass and cost are
You won the contract. The first batch of springs delivered to connect the absorber to the radar
system where incorrectly manufactured, such that 1mm free-play was introduced. You have to
analyse the new system and provide the bounds of vibration for the system. You have also been
asked to provide an equivalent linear system and its accuracy.
Hint 1: Common practice to reduce vibration is to add another mass/spring damper system tuned
at the natural frequency of the original system
Hint 2: First order harmonic balance allows for the system to be linearised
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I am working on modelling and simulations of vehicles. I have strong knowledge in dynamics of the system and also good in electrical. This system can be modelled in MATLAB/Simulink