In damped harmonic motion, we calculate damping coefficient γ by comparing the periods of damped and undamped motion. For the given situation where the quasi-period is 90% greater than the undamped period, the damping coefficient is approximately 0.7416.
The subject of this question involves Damped Harmonic Motion, a concept in Physics, related to vibrations and waves. The equation given, u'' + γu' + u = 0, describes the motion where γ denotes the damping coefficient. Here, we have to calculate this damping coefficient when the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion.
To solve this, we must use the relationship between damped and undamped periods. The quasi-period T' of a damped harmonic motion relates to the undamped period T as: T' = T/(sqrt(1 - (γ/2)^2)). Now, given that T' = 1.9T, we can but these two equations together:
1.9 = 1/(sqrt(1 - (γ/2)^2))
Solving this for γ, we get γ ≈ 0.7416. Hence, the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion is approximately 0.7416.
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The value of the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the undamped motion is the one that satisfies γ=2*ω*0.9, where ω is the natural frequency of oscillation.
The given equation is for a damped harmonic oscillator, a physical system that oscillates under both a restoring force and a damping force proportional to the velocity of the system. The damping coefficient γ determines the behavior of the system and in this case, we need to find the value of γ such that the quasi period of the damped motion is 90% greater than the period of the undamped motion.
The period of the undamped motion, T₀, is calculated by the formula T₀=2π/sqrt(ω), where ω is the natural frequency of oscillation. The quasi period of the damped motion, Td, is increased by a factor of 1+η (in this case, 1.9 as the increase is 90%) and calculated by the formula Td=T₀(1+η) = T₀*1.9.
The damping ratio η is determined by the damping coefficient γ as η=γ/2ω. Therefore, by combining these expressions and rearranging the terms, we extract γ from these formulas as γ=2ω*η => γ=2*ω*(0.9). Thus, the value of the damping coefficient γ for which the quasi period of the damped motion is 90% greater than the period of the corresponding undamped motion is the one which satisfies γ=2*ω*0.9.
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Answer:
right angle and congruent
Step-by-step explanation:
Answer:
In the given shapes above, we can see that all shapes have four sides.
Above geometrical shapes could be named as Rectangles, parallelogram or quadrilateral.
First two shapes are Rectangles.
Third is a parallelogram.
Fourth and fifth shapes are Rectangles again.
Also we can say all those shapes with four side as quadrilaterals. (Note: A quadrilateral has four sides.)
Below shown shape has only three sides in it.
It is called a triangle when a shape has three sided close figure.
So, we could drag : Not similar - Different Type of shape.
Which of these sentences is always true for a parallelogram?
Answer:
parallelograms are shapes that have 2 sets of parallel sides. for example, squares, rectangles, and rhombuses are all types of parallelograms
Answer:
50
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The distance between the friends is changing at the constant rate of 50 mph.
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The equation for the distance in the westerly direction is ...
w = 30t . . . . . miles, where t is time in hours
The equation for the distance in the southerly direction is ...
s = 40t . . . . . miles, where t is time in hours
Then the total distance between the friends is ...
d = √((30t)² + (40t)²) = √(2500t²) = 50t . . . . miles, where t is time in hours
And the rate of change of distance is the derivative of this with respect to t:
dd/dt = 50 . . . . . . miles per hour