Solution HW#2
1
2
3. The characteristic equation of a single-degree-of-freedom vibration system has two real roots -3 and -8. If
the initial displacement is 1 and initial velocity is zero, what is the free vibration solution?
x (t ) = C1e 3t + C2 e 8t ; x
Homework #1
1.
Please formulate the equation of motion of the
following system.
T
Fee-t
J0
k2r
External force
m
k1x
T
Fe e t T k1 x = mx => mx + k1 x = Fe e t T (+ up) (1)
T (2r ) k 2r 2 = J 0 => J 0 + k 2r 2 = 2rT (+ clockwise) (2)
Multiplying (1) by 2r
Homework 4
1. The landing gear of an airplane, m = 2,000 kg, k = 5*106 N/m, and c = 158,805 N*s/m, can be idealized as
the spring-mass-damper system shown in the figure below. If the runway surface is described y(t) =
0.2cos(157.08t) m, determine the stea
Solution
1.
2.
a. Given n = 20 rad/s and st = 0.05 m, the frequency ratio = 0.5.
6
From the frequency-response figure, the magnification factor
(X/st) ~ 1.32; from the phase-angle figure, the phase lag is ~ 7.55 degrees ~ -0.132 radian.
Magnification fact
1, A single-degree-of-freedom vibration system with m = 10 slug, c = 1.2 lb s/ft, and k = 40 lb/ft find its
damping ratio and undamped natural frequency. (10%)
Answer: damping ratio
0.03
, undamped natural frequency
2 rad/s
(with unit)
(Show steps)
n = k
Consider the ow of an incompressible uid between two parallel plates separated by a distance 2H. If the velocity
prole is given by:
2
cfw_13
where a: is the centerline velocity, determine the average velocity of the ow, a . Assume the depth into the page
"I?
4' amt 3 '
TOTAL (3 points)
on,
By how much is the thrust force (along the centerline of the a/c) reduced for the case
indicated compared to normal ight when the exhaust is parallel to the centerline?
(1 point)
2) Two water jets equal size and spW
UNIVERSITY OF CENTRAL FLORIDA
Mechanical & Aerospace Engineering Department
Fluid mechanics EML 3701
QUIZ 1
1) Derive the unit (SI) for dynamic viscosity () using Newtons law of
viscosity ( =
).
(1 point)
2) Determine the magnitude (in terms of , U and h
UNIVERSITY OF CENTRAL FLORIDA
Mechanical & Aerospace Engineering Department
Fluid mechanics EM]. 3701
QUIZ6
1)
b
An incompressible viscous uid is placed between two arge parallel
plates as shown above. The bottom plate is xed and the upper plate
moves w
UNIVERSITY OF CENTRAL FLORIDA
Mechanical & Aerospace Engineering Department
Fluid mechanics EML 3701
MIDTERM 2 (20 + 2 POINTS)
- Please show all your steps in your calculations
QUESTION 1 (5 points):
a)
b)
c)
Is the flow steady or unsteady? (1 point)
Is t
756 Consider fullr developed Couetle owow between
two innite parallel plates separated by distance h, with the
top plate moving and the bottom plate stationary,r as illus-
trated in Fig. Ill56. The ow is steady, incompressible, and
two-dimensional in the
UNIVERSITY OF CENTRAL FLORIDA
Mechanical .5 Ampaee Engineering Department
Fluid mechanics EML 3701
QUIZ 12
"ii-Fm
31 hr M
.b.
Far a planar Pom-die ow, the uid velocity in the xdirection is given by;
I =;(-:5)(i)[ at)
I) Find 3 (in menu: which 5, is maximu
QUIZ 5 (2.5 POINTS)
1) If a stone with a mass of 40 lg is to be weighed 200 N in the water. Find
the volume and densi of the stone?
(1 point)
2) Object K with 2V volume is oating in X liquid with half of its volume
immersed in the liquid. If another objec
QUIZ 2
1) What is the unit for kinematic viscosity (v)? (in SI units)
(0.5 points)
2) The upper plate is moving right with a velocity of 3 m/s;
while the bottom plate is stationary. The top fluid (fluid 1)
puts a shear stress on the upper plate, and the l
Quiz 1
Sam, a biologist, was told by a friend that the electric power company was able to create
electricity to be used in homes. Sam said that this was impossible because _. (0.5 points)
1)
A)
B)
C)
D)
another form
E)
2)
3)
energy can be created but not
QUIZ 4 (3.5 points)
1) (1 point)
Find h if the specific gravity (SG) of
OIL = 0.78. What happens to the h
value if water is used instead of oil?
SG=
oil
water
2) (2.5 point)
If a man with a height of 180 cm
immersed in pure water in a standing
condition.
1) ( a = 4i - 4j ft/s2 and IaI = 5.66 ft/s2)
2) Repeat problem 1:
( a = 36i + 36j ft/s2 and IaI = 50.9 ft/s2)
3) (ax =x; ay=2x2z+x2yz; az=x2z2+y2z)
4) (a 0 ; b w = - (y/2 + z) I + 5/2 z j y/2 k , NO)
5) (3xy2) k ; NO
6) (NO; none except both a and b is eq
QUIZ 3
1) True/False statements (1.5 points, each 0.25)
a) Liquids tend to minimize their surface area (TRUE)
b) Molecules on the surface of the liquid have fewer molecules to
interact with (TRUE)
c) As the temperature of a liquid increases, intermolecula
UNIVERSITY OF CENTRAL FLORIDA
Mechanical & Aerospace Engineering Department
Fluid mechanics EML 3701
QUIZ 2
1) Define the following terms with their SI units.(1 point)
a)
b)
c)
d)
e)
Dynamic (Absolute) viscosity: (kg/m s)
Shear strain (for fluids): (1/s)