Solution
Assuming small displacements we obtain Free body diagram as shown below.
Taking anti clockwise rotation as poistive, we get,
Substituting the values we get,
For steady state solution,let's assume
, ,
Therefore this is the expression for steady state amplitude when system is excited with . Variation of steady state amplitude for various values of can be observed from the plot shown below.
Natural frequency
Take,
Solving this we get natural frequency ,
Displacements
a) Maximum displacement in the range 0 to 3 Hz occurs at 3 Hz
b) Maximum displacement in the range 3 to 10 Hz occurs at natural frequency , i.e, 5.908 Hz
c) Maximum displacement above 10 Hz occurs at 10 Hz
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