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2 answers:
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Answer:
The relationship is only between the coefficients A, E and J which is:
. The remaining coefficients can be anything without any constraints.
Explanation:
Given:
The three components of velocity is a velocity field are given as:
The fluid is incompressible.
We know that, for an incompressible fluid flow, the sum of the partial derivatives of each component relative to its direction is always 0. Therefore,
Now, let us find the partial derivative of each component.
Hence, the relationship between the coefficients is:
There is no such constraints on other coefficients. So, we can choose any value for the remaining coefficients B, C, D, F, G and H.
Answer:
The maximum acceleration of the system is 359.970 centimeters per square second.
Explanation:
The motion of the mass-spring system is represented by the following formula:
Where:
- Position of the mass with respect to the equilibrium position, measured in centimeters.
- Amplitude of the mass-spring system, measured in centimeters.
- Angular frequency, measured in radians per second.
- Time, measured in seconds.
- Phase, measured in radians.
The acceleration experimented by the mass is obtained by deriving the position equation twice:
Where the maximum acceleration of the system is represented by .
The natural frequency of the mass-spring system is:
Where:
- Spring constant, measured in newtons per meter.
- Mass, measured in kilograms.
If and
, the natural frequency is:
Lastly, the maximum acceleration of the system is:
The maximum acceleration of the system is 359.970 centimeters per square second.