A certain vibrating system satisfies the equation . Find the value of the damping coefficient for which the quasi period of the
damped motion is greater than the period of the corresponding undamped motion. Round you answer to three decimal places.
1 answer:
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Answer:
See Explanation Below
Step-by-step explanation:
The question is incomplete (because the figure to calculate the perimeter is missing).
However from the comment attached to your question, I understand that the figure looks like a plus sign.
The perimeter of a plane shape is calculated by adding the length of each side of the shape.
Take for instance;
A square of length 5cm.
We know that a square has 4 equal sides; meaning that the length of the other sides are also 5cm
So, the perimeter of the square will be calculated as 5cm + 5cm + 5cm + 5cm = 20cm
Similarly, the perimeter of a triangle whose sides are 4ft, 3ft and 5ft will be calculated by adding up the length of the three sides.
Perimeter of the triangle = 4ft + 3ft + 5ft
Perimeter = 12ft.
Having explained how the perimeter of a plane shape is calculated; take for example, the attachment below.
(The sides are measured in centimetres)
The plus sign has 12 sides; Its perimeter is calculated by adding up the length of the 12 sides.
Perimeter = 3 + 7 + 7 + 5 + 5 + 5 + 5 + 2 + 2 + 4 + 4 + 3
Perimeter = 52cm
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.