The free oscillations of a mechanical system are observed to have a certain angular frequency w....

 

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The free oscillations of a mechanical system are observed to have a certain angular frequency w₁. The same system, when driven by a force Fo cos wt (where Fo= const. and wis variable), has a power resonance curve whose angular frequency width, at half-maximum power, is w1/5. (a) At what angular frequency does the maximum power input occur? (b) What is the Q of the system? (c) The system consists of a mass m on a spring of spring constant In terms of m and k, what is the value of the constant b in the resistive term-bv? (d) Sketch the amplitude response curve, marking a few char- acteristic points on the curve. The free oscillations of a mechanical system are observed to have a certain angular frequency w₁. The same system, when driven by a force Fo cos wt (where Fo= const. and wis variable), has a power resonance curve whose angular frequency width, at half-maximum power, is w1/5. (a) At what angular frequency does the maximum power input occur? (b) What is the Q of the system? (c) The system consists of a mass m on a spring of spring constant In terms of m and k, what is the value of the constant b in the resistive term-bv? (d) Sketch the amplitude response curve, marking a few char- acteristic points on the curve.

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