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There is no generic "vibration" equation, as many different things can vibrate with many different boundary conditions. There is, however, a generic wave equation which, as I just hinted at, can be used to formulate equations for specific vibrations.

Given a function u(x,y,z,t) where x, y, and z are spatial coordinates in Euclidean space and t is time, the wave equation is given as:

∂2u/∂t2 = vp2∇2u,

where vp is the phase velocity of the wave and ∇2 is the Laplacian.

For the specific example of a vibrating string with a small amplitude, the wave equation becomes:

∂2y/∂t2 = v2∂2y/∂x2,

where y(x,t) and v is the velocity of the wave.

The remarkable thing about the wave equation is how often Mother Nature uses it. The "u(x,y,z,t)" can describe the vibration of a drum head, the electromagnetic fields of light, the ripples on water, the sound of your voice and much more.

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Ashlee Farrell

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2y ago
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AnswerBot

6mo ago

The vibration equation describes the behavior of a vibrating system, typically in mechanical engineering. It takes into account factors like mass, stiffness, and damping to predict the motion of the system over time. The equation can be represented in various forms depending on the specific characteristics of the vibrating system being analyzed.

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The partial differentiation equation for the vibration of a uniform curved elastic plate is of fundamental importance and is known after her name Who is she?

Sophie germain


What is the vibration equation?

There is no generic "vibration" equation, as many different things can vibrate with many different boundary conditions. There is, however, a generic wave equation which, as I just hinted at, can be used to formulate equations for specific vibrations.Given a function u(x,y,z,t) where x, y, and z are spatial coordinates in Euclidean space and t is time, the wave equation is given as:∂2u/∂t2 = vp2∇2u,where vp is the phase velocity of the wave and ∇2 is the Laplacian.For the specific example of a vibrating string with a small amplitude, the wave equation becomes:∂2y/∂t2 = v2∂2y/∂x2,where y(x,t) and v is the velocity of the wave.The remarkable thing about the wave equation is how often Mother Nature uses it. The "u(x,y,z,t)" can describe the vibration of a drum head, the electromagnetic fields of light, the ripples on water, the sound of your voice and much more.


What has the author Harry Melvin Shoemaker written?

Harry Melvin Shoemaker has written: 'A generalized equation of the vibrating membrane expressed in curvilinear coordinates' -- subject(s): Vibration


What is the equation for the for the loud squeaky pop?

The equation for the loud squeaky pop can be described as a high-frequency sound wave with a sudden increase in amplitude, resulting in a sharp and piercing noise. This sound can be represented using equations that describe the vibration frequency and intensity of the sound wave.


What part of speech is vibration?

Vibration is a noun.


What is the vibration?

There is no generic "vibration" equation, as many different things can vibrate with many different boundary conditions. There is, however, a generic wave equation which, as I just hinted at, can be used to formulate equations for specific vibrations.Given a function u(x,y,z,t) where x, y, and z are spatial coordinates in Euclidean space and t is time, the wave equation is given as:∂2u/∂t2 = vp2∇2u,where vp is the phase velocity of the wave and ∇2 is the Laplacian.For the specific example of a vibrating string with a small amplitude, the wave equation becomes:∂2y/∂t2 = v2∂2y/∂x2,where y(x,t) and v is the velocity of the wave.The remarkable thing about the wave equation is how often Mother Nature uses it. The "u(x,y,z,t)" can describe the vibration of a drum head, the electromagnetic fields of light, the ripples on water, the sound of your voice and much more.


How would you describe vibration?

mainly two types of Vibration measurement: shaft vibration Bearing Vibration


What is the abbreviation of vibration?

The abbreviation for vibration is "vib."


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Use vibration dampening measures like a barsnake.


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