The derivation of damped frequency and natural frequency formula

Thread starter tingyuau
Start date Sep 27, 2012
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Damped Derivation Formula Frequency Natural Natural frequency

In summary, the damped frequency formula is derived from the equation of motion for a damped harmonic oscillator and is used to describe the behavior of damped systems in physics. It is related to the natural frequency formula, with the natural frequency being a special case where there is no damping present. The damped frequency is affected by the mass, stiffness, and damping coefficient of a system, and it is commonly used in real-world applications such as engineering and the development of various devices.

Sep 27, 2012

tingyuau

Can someone derive for me the equation ω_d=ω_nsqrt(1-ζ²)

Thanks

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Sep 27, 2012

nasu

Homework Helper

Yes.

http://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_harmonic_oscillator

What is the derivation of the damped frequency formula?

The damped frequency formula is derived from the equation of motion for a damped harmonic oscillator. It is obtained by solving the equation of motion using the method of undetermined coefficients and considering the effects of damping on the system.

What is the significance of the damped frequency formula in physics?

The damped frequency formula is used to describe the behavior of damped harmonic oscillators, which are common in many physical systems. It helps us understand how damping affects the natural frequency of a system and how it impacts the amplitude and phase of the oscillations.

How is the natural frequency formula related to the damped frequency formula?

The natural frequency formula is a special case of the damped frequency formula, where the damping coefficient is equal to zero. This means that there is no damping present in the system and the natural frequency is equal to the damped frequency.

What factors affect the damped frequency of a system?

The damped frequency of a system is affected by the mass of the object, the stiffness of the spring, and the damping coefficient. Increasing the mass or stiffness will decrease the damped frequency, while increasing the damping coefficient will increase the damped frequency.

How is the damped frequency formula used in real-world applications?

The damped frequency formula is used in various fields such as engineering, physics, and mathematics to analyze and design systems that involve damped harmonic oscillations. It is also used in the development of devices such as shock absorbers, musical instruments, and suspension systems.