Compute the solution to x + 2x + 2x = 0 for Xo = 0 mm, vo = 1 mm/s and write down the closed-form expression for the response.
1 answer:
Answer:
β = = 0.7071 ≈ 1 ( damping condition )
closed-form expression for the response is attached below
Explanation:
Given : x + 2x + 2x = 0 for Xo = 0 mm and Vo = 1 mm/s
computing a solution :
M = 1,
c = 2,
k = 2,
Wn = =
next we determine the damping condition using the damping formula
β = = 0.7071 ≈ 1
from the condition above it can be said that the damping condition indicates underdamping
attached below is the closed form expression for the response
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Solution :
The percentage of the students who have a chance of repeating their current year = 3%
The drop out students for the first year and the sophomores = 6%
Drop out rate of first year and the seniors = 4%
Now for the state space :
S = { first year(1), sophomores(2), juniors(3), seniors(4), graduates(G), Dropouts(D) }
Therefore
the first year students are indicated as '1'
Sophomores are indicated as '2'
Juniors are indicated as '3'
Seniors are indicated as '4
Graduates are indicated as 'G'
Dropouts are indicated as 'D'
The transition diagram is attached below.
The probability of the students who have the chance of repeating their current year = 3/100 = 0.03
Probability of first year dropouts and sophomores = 6/100 = 0.06
Probability of dropout rate of juniors and seniors = 4/100 = 0.04
Therefore, the probability matrix can be made as :
1 2 3 4 G D
Here, G represents 'graduates' and D represents 'Dropouts.'
Answer:
1. Graph C
2. Friction
Explanation:
1. The line on all of the graphs shown represents velocity. The formula for velocity is where d is distance and t is time. Focusing on the first lap, the starting point on the graph should be the origin and the "ending" point should be (20, 3). These requirements eliminate graph A as an answer because its "end" is not (20, 3). During the break, the student does not move, so the slope of the line should be completely horizontal. The break lasted for 5 minutes, so the correct graph should have a horizontal line between the points (20, 3) and (25, 3). This requirement eliminates graph B and D because their break is either not long enough (B) or too long (D).
2. Friction slows down the movement of objects. When an object is rough, it produces more friction which causes the object to be slowed more. When an object is smooth, friction slows it less than it would for a rough object.