Question

An electronic instrument is to be isolated from a panel that vibrates at frequencies ranging from 25 Hz to 35 Hz. It is estimated that at least 80 percent vibration isolation must be achieved to prevent damage to the instrument. If the instrument weights 85 N, find the static deflection of the isolator.

Answer 1

To calculate the static deflection of an isolator, you need to determine the natural frequency of the system and use the formula Static Deflection = (Weight of the Instrument / Spring Constant) / (2 * Pi * Natural Frequency).

To calculate the static deflection of the isolator, you need to determine the natural frequency of the system and then calculate the static deflection using the formula:

Static Deflection = (Weight of the Instrument / Spring Constant) / (2 * Pi * Natural Frequency)

The natural frequency can be calculated using the formula:

Natural Frequency = sqrt(Spring Constant / Mass)

To find the spring constant, you need to determine the resonant frequency range and the required vibration isolation. The resonant frequency range is given as 25 Hz to 35 Hz, and the required vibration isolation is at least 80 percent. Using these values, you can calculate the spring constant:

Spring Constant = (2 * Pi * (35 + 25) / 2) * (2 * Pi * (35 - 25) / 2) * (0.8^2)

Finally, substitute the values into the formula for static deflection to find the answer.