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An instrument has a natural frequency of 10 Hz. Maximum acceleration of the system is observed to be 24 m/s2. The maximum displacement of the system is ....mm.
(Important - Enter only the numerical value in the answer)
Correct answer is between '6,6.1'. Can you explain this answer?
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An instrument has a naturalfrequency of 10 Hz. Maximumacceleration of ...
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An instrument has a naturalfrequency of 10 Hz. Maximumacceleration of ...
The natural frequency of an instrument is the frequency at which it tends to vibrate when disturbed. In this case, the natural frequency is given as 10 Hz.
The maximum acceleration of the system is observed to be 24 m/s^2. This means that when the instrument is vibrating at its natural frequency, the maximum acceleration it experiences is 24 m/s^2.
To determine the maximum displacement of the system, we can use the formula for the maximum displacement of a vibrating system:
Amplitude = (Maximum acceleration) / (Angular frequency)^2
The angular frequency (ω) of a system is given by the formula:
Angular frequency (ω) = 2π × (Natural frequency)
Substituting the given values, we have:
Angular frequency (ω) = 2π × 10 Hz = 20π rad/s
Now, we can calculate the maximum displacement using the formula mentioned earlier:
Amplitude = (24 m/s^2) / (20π rad/s)^2
Simplifying further:
Amplitude = (24 m/s^2) / (400π^2 rad^2/s^2)
Amplitude ≈ 6.08 mm (rounded to two decimal places)
The correct answer is between 6 and 6.1 mm.
In summary, the maximum displacement of the system is approximately 6.08 mm when the instrument is vibrating at its natural frequency of 10 Hz and experiencing a maximum acceleration of 24 m/s^2.
The maximum acceleration of the system is observed to be 24 m/s^2. This means that when the instrument is vibrating at its natural frequency, the maximum acceleration it experiences is 24 m/s^2.
To determine the maximum displacement of the system, we can use the formula for the maximum displacement of a vibrating system:
Amplitude = (Maximum acceleration) / (Angular frequency)^2
The angular frequency (ω) of a system is given by the formula:
Angular frequency (ω) = 2π × (Natural frequency)
Substituting the given values, we have:
Angular frequency (ω) = 2π × 10 Hz = 20π rad/s
Now, we can calculate the maximum displacement using the formula mentioned earlier:
Amplitude = (24 m/s^2) / (20π rad/s)^2
Simplifying further:
Amplitude = (24 m/s^2) / (400π^2 rad^2/s^2)
Amplitude ≈ 6.08 mm (rounded to two decimal places)
The correct answer is between 6 and 6.1 mm.
In summary, the maximum displacement of the system is approximately 6.08 mm when the instrument is vibrating at its natural frequency of 10 Hz and experiencing a maximum acceleration of 24 m/s^2.
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