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1(a) A damped simple harmonic oscillator has mass 2.0 kg, spring constant 50 N/m, and mechanical resistance 0.80 kg/s. The force Fcos(@t) is exerted on the mass, where F = 3.0 N and o = 5.1 rad/s. Determine the quality factor of the oscillator. The bandwidth of an oscillator is the frequency range over which the dissipated power is equal to or greater than half of the maximum value. Does the drive frequency lie within the bandwidth of the oscillator? As always, show your work.

1(a) A damped simple harmonic oscillator has mass 2.0 kg, spring constant 50 N/m, and mechanical resistance 0.80 kg/s. The force Fcos(@t) is exerted on the mass, where F = 3.0 N and o = 5.1 rad/s. Determine the quality factor of the oscillator. The bandwidth of an oscillator is the frequency range over which the dissipated power is equal to or greater than half of the maximum value. Does the drive frequency lie within the bandwidth of the oscillator? As always, show your work.

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1(a) A damped simple harmonic oscillator has mass 2.0 kg, spring constant 50 N/m, and mechanical resistance 0.80 kg/s. The force Fcos(@t) is exerted on the mass, where F = 3.0 N and o = 5.1 rad/s. Determine the quality factor of the ocillator. The bandwidth of an oscillator is the frequency range over which the dissipated power is equal to or greater than half of the maximum value. Does the drive frequency lie within the bandwidth of the oscillator? As always, show your work. (b) The drive frequency in (a) is now slowly changed to o = 0.2 rad/s. What is this regime called (stiffness-controlled, inertia-controlled, or resistance-controlled)? Determine the approximate values of the displacement amplitude and the phase of the displacement relative to the force (not the velocity relative to the force).
Transcribed Image Text:1(a) A damped simple harmonic oscillator has mass 2.0 kg, spring constant 50 N/m, and mechanical resistance 0.80 kg/s. The force Fcos(@t) is exerted on the mass, where F = 3.0 N and o = 5.1 rad/s. Determine the quality factor of the ocillator. The bandwidth of an oscillator is the frequency range over which the dissipated power is equal to or greater than half of the maximum value. Does the drive frequency lie within the bandwidth of the oscillator? As always, show your work. (b) The drive frequency in (a) is now slowly changed to o = 0.2 rad/s. What is this regime called (stiffness-controlled, inertia-controlled, or resistance-controlled)? Determine the approximate values of the displacement amplitude and the phase of the displacement relative to the force (not the velocity relative to the force).
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