- #1
tingyuau
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Can someone derive for me the equation ωd=ωnsqrt(1-ζ2)
Thanks
Thanks
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.
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.
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.
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.
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.