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An input signal oscillates sinusoidally between 12V and 24V with a frequency of 120Hz. It is measured with an instrument having a damping ratio of 0.7, a damped ringing frequency of 250Hz, and static sensitivity of 1V/V. Determine the magnitude of the output signal components.

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Final answer:

The magnitude of the output signal components can be determined using the damping ratio, damped ringing frequency, and static sensitivity. The output signal exhibits attenuated oscillations due to the damping ratio. The magnitude is computed using the static sensitivity and input signal.

Step-by-step explanation:

The magnitude of the output signal components can be determined using the concept of damping ratio, damped ringing frequency, and static sensitivity. The damping ratio (ξ) of 0.7 indicates that the output signal will be attenuated, but will still exhibit oscillations. The damped ringing frequency (fr) of 250Hz is the frequency at which the output signal oscillates. The static sensitivity (S) of 1V/V means that for every 1V change in the input signal, the output signal will change by 1V as well.

To determine the magnitude of the output signal components, we can use the formula:

Output Signal = Static Sensitivity x Input Signal x Magnitude Factor

The magnitude factor is calculated using the formula:

Magnitude Factor = sqrt(1 + (2ξ * (f - fr) / fr)^2)

Substituting the given values:

Input Signal = 24V - 12V = 12V

Frequency (f) = 120Hz

Magnitude Factor = sqrt(1 + (2 * 0.7 * (120 - 250) / 250)^2) = 0.738

Output Signal = 1V/V x 12V x 0.738 = 8.856V

Therefore, the magnitude of the output signal component is approximately 8.856V.

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