# Harmonic Vibration-Is any data missing here

• jrm2002
In summary, a damped spring mass system with a force of 2520 lb., stiffness of 89,000 lb/inches, and damping constant of 112 lb.sec/inches is studied. The natural frequency and damping ratio can be determined using equations, while the amplitude of the exciting force can be found when given the peak amplitude of the vibrating mass. The amplitude of the vibrating mass can be calculated using the frequency ratio and amplitude of the vibrating mass. Additional help can be found in the provided link.
jrm2002

## Homework Statement

A structure modeled as a damped spring mass system with mg=2520 lb., k= 89,000 lb/inches,and damping constant c = 112 lb.sec/inches is subjected to a harmonic exciting force.
Determine a)Natural frequency
b)Damping ratio
c)Amplitude of the exciting force when the peak amplitude of of of the vibrating mass is measured to be 0.37 inches.
d)The Amplitude of the exciting force when the amplitude
measured at the peak frequency assumed to be resonant
frequency.

## Homework Equations

a)Natural frequency can be determined as the ratio of the square root of stiffness to mass
b)Damping ratio is the ratio of the damping coefficient to critical damping
(2*m*natural frequency)

## The Attempt at a Solution

Considering the question (c)

To get, Amplitude of the exciting force when the peak amplitude of the vibrating mass is measured to be 0.37 inches.
Now, amplitude of the vibarating mass is a function of frequency ratio(forcing frequency to natural frequency) as well as the amplitude of the vibrating mass?

So how to obtain the amplitude of the vibrating mass??

Similarly question(d)??

## 1. What is harmonic vibration?

Harmonic vibration is a type of oscillatory motion in which the displacement of an object from its equilibrium position is directly proportional to the force acting on it. This means that the object will vibrate back and forth in a periodic manner with a constant frequency.

## 2. How is harmonic vibration measured?

Harmonic vibration can be measured using various instruments such as accelerometers, seismometers, and vibrometers. These instruments measure the acceleration, velocity, or displacement of the vibrating object and provide data that can be used to analyze the harmonic motion.

## 3. What factors affect harmonic vibration?

The factors that affect harmonic vibration include the mass of the vibrating object, the stiffness of the material, and the frequency of the applied force. Changes in any of these factors can alter the amplitude and frequency of the vibration.

## 4. Is any data missing in the study of harmonic vibration?

It is possible that some data may be missing in the study of harmonic vibration due to limitations in the measuring instruments or experimental setup. However, with advanced technology and improved techniques, it is possible to minimize the missing data and obtain accurate results.

## 5. How is harmonic vibration used in real-world applications?

Harmonic vibration has various applications in different fields such as engineering, music, and medicine. In engineering, it is used to design structures and machines that can withstand harmonic vibrations without failure. In music, it is used to create different sounds and tones. In medicine, it is used in diagnostic tools such as ultrasound machines and MRI scanners.

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