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PRACTICE PROBLEMS

1. Develop a transfer function for the system pictured below and then find the response to an input voltage of Vi = 10sin(1,000,000 t) using phasor transforms.

2. A single d.o.f. model with a weight of 1.2 kN and a stiffness of 340 N/m has a steady-state harmonic excitation force applied at 95 rpm (revolutions per minute). What damper value will give a vibration isolation of 92%? Use phasors to do the calculations.

3. Four helical compression springs are used, one at each corner of a piece of equipment. The spring rate is 240 N/m for each spring and the vertical static deflection of the equipment is 10mm. Calculate the mass of the equipment and determine the amount of isolation the springs would afford if the equipment operating frequency is twice the natural frequency of the system.

4. a) For the circuit below find the transfer function and the steady state response for an input of Vi=5sin(1000t)V.

b) Verify the results in part a) by explicitly solving the differential equation.

5. Given an input of F=5sin(62.82t), find the output, x, using phasors for the following transfer functions.