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
Answer:
Please see the attached file for the complete answer.
Explanation:
Boats float because the gravity is acting down on it and the buoyant force is acting up on the ship.
Answer:
155fts
Explanation:
We apply the bernoulli's equation to get the depth of water.
We have the following information
P1 = pressure at top water surface = 0
V1 = velocity at too water surface = 0
X1 = height of water surface = h
Hf = friction loss = 0
P2 = pressure at exit = 0
V2 = velocity at exit if penstock = 100ft/s
X2 = height of penstock = 0
g = acceleration due to gravity = 32.2ft/s²
Applying these values to the equation
0 + 0 + h = 0 + v2²/2g +0 + 0
= h = 100²/2x32.2
= 10000/64.4
= 155.28ft
= 155
