Final Test: Physics 3C- Spring 2012
Name_; #ID_
Multiple Choices: 4% each
1. What is the maximum value of the acceleration a when x = A cos ( t + ) ?
a.
b. t
c. 2 A
d. A
e. A
2. A 500 Hz tone is sounded at a train station as a train moves toward the sta
1. Signals
a. Generation and synthesis
b. Basic analysis
i. Frequency domain (fourier transform
ii. Time domain (filter, detrending, event counting
2. Images
a. Basic (types, pixel resolution, interpretation
b. Base pressuring ( intro to pr functions, bin
Physics 3B Quiz Student Name:
Discussion (circle one)
_
8am 9am 10am
12pm
1pm 2pm 3pm 4pm 5pm 6pm
PROBLEM: Airplane wings are designed to make air flow faster below the wing than
the air above the wing. This creates a difference in pressure. Consider a ve
Physics 3B Quiz Hwk#4
Student Name: _
ID#: _
Discussion (circle one)
8am 9am 10am 11am
12pm
1pm 2pm 3pm 4pm 5pm 6pm
PROBLEM: A single proton sits at the origin (0, 0) of a plane. Calculate the magnitude
and direction of the Electric field at the point (2,
Physics 3B Quiz Hwk#2
Student Name: _Solution_
ID#: _
Discussion (circle one)
8am 9am 10am 11am
12pm
1pm 2pm 3pm 4pm 5pm 6pm
PROBLEM: Consider a building as if it were a solid cube of concrete, with a length of
10 m on each side. At night, the concrete co
Physics 3B Quiz Hwk#9
Student Name: _Solution_
ID#: _
Discussion (circle one)
8am 9am 10am 11am
12pm
1pm 2pm 3pm 4pm 5pm 6pm
PROBLEM: The diagram below shows a frictionless bar, traveling to the right on an
open loop in a 6 T magnetic field. The bar has a
Physics 3B Quiz Hwk#8
Student Name: _Solution_
ID#: _
Discussion (circle one)
8am 9am 10am 11am
12pm
1pm 2pm 3pm 4pm 5pm 6pm
PROBLEM: An electron is moving through a magnetic field. At one point along its
r
6
i
trajectory, the electron has a velocity v =
Physics 3B Quiz Hwk#7
Student Name: _
ID#: _
Discussion (circle one)
8am 9am 10am 11am
12pm
1pm 2pm 3pm 4pm 5pm 6pm
PROBLEM: A circuit contains a battery connected in series with a 50k resistor, a 5
F capacitor with a full charge of 10.0 C, and an open sw
Physics 3B Quiz Hwk#5
Student Name: _SOLUTION_
ID#: _
Discussion (circle one)
8am 9am 10am 11am
12pm
1pm 2pm 3pm 4pm 5pm 6pm
PROBLEM: A plastic ball is suspended by a very light string, 40 cm long. The ball
has a charge of +10 C and is displaced in a unif
Physics 3B Quiz Hwk#6
Student Name: _SOLUTION_
ID#: _
Discussion (circle one)
8am 9am 10am 11am
12pm
1pm 2pm 3pm 4pm 5pm 6pm
PROBLEM: A charged particle is accelerated from rest in a uniform electric field.
After it has passed through a potential differen
1.
Fluids (8 pts)
3
a. A hot-air balloon is to lift a payload of 175 kg. If the balloons volume is 4500 m and the air outside
the balloon is at STP, to what temperature must the air in the balloon be heated? (The density of air
-3
3
at STP is 1.2910 kg/m
Physics 3B Final Exam Formula Sheet
Resistance and Resistivity:
R=
Bernoullis Equation:
+
+
=
+
+
Maxwell-Boltzmann distribution function:
=4
Work done on ideal gas in isothermal process:
=
ln / )
(
Stefans Law:
=
Coulombs Law:
k qq
F12 = e 12 2
Physics 3c: Midterm (2:00-3:20 pm, May 1, 2012)
Name_ID_Discussion Setion_
Multiple choices (4 % each):
1. A body oscillates with simple harmonic motion along the x-axis. Its displacement
varies with time according to the equation x = 5 sin t + . The vel
Review
Physics 3c for materials a4er the midterm
Chapters 33, 34, 35, 36, 37 and 41.
Some materials not in this le may also appear in the test.
You should also review materials before the midterm
Oce hours
Physics 2 Tutorial Week 1
September 28, 2016
1. Nyan the cat can meow at a rate of 20 meows in 5 seconds. If Nyan meows
for 3 minutes and 36 seconds, how many total meows will Nyan the cat have
performed during this time?
Solution:
(a) Find the rate R at
Lesson One: Greetings
Part One
(Dialogue I: Exchanging Greetings)
I. Listening Comprehension
A.
( d ) 1.
( b ) 2.
( a ) 3.
B.
( c ) 1.
C.
( d ) 1.
( b ) 2.
III. Reading Comprehension
A.
( T ) 1.
( F ) 2.
B.
(F) 1.
(T) 2.
( F ) 3.
(T) 3.
( T ) 4.
(F) 4.
IV
Solution of a linear first-order ODE (chap6)
On page 42 of the textbook, once we write down the integrating factor I(x) by formula (6.2),
we solve the resulting new ODE (6.3), the solution of (6.3) is also the solution of the original ODE.
There is no for
Table 1: Final Exam Table of Laplace Transforms
f (x) = L1 cfw_F (s)
F (s) = Lcfw_f (x)
1
1
s
eax
1
sa
xn , n is positive integer
n!
sn+1
xp , p > 1
(p+1)
,
sp+1
sin(ax)
a
s2 +a2
cos(ax)
s
s2 +a2
eax sin(bx)
b
(sa)2 +b2
eax cos(bx)
sa
(sa)2 +b2
xn eax , n
c
Yue
Zhang
Final practice problems
1. Solve: y 00 y 0 = 3 + cos x.
ex
2. Solve: y 00 2y 0 + y = 2
.
x +1
3. Solve by using L (Laplace transform):
y 00 y 0 = x + sin x, y(0) = 0, y 0 (0) = 0
4. Solve by using L (Laplace transform):
y 00 y 0 2y = ex U (x 2
c
Yue
Zhang
Brief notes on Chap 11
Goal: Solve L(y) = (x) when (x) has a certain form.
Step 1: Solve the complementary solution yh , this is the solution of L(y) = 0.
Step 2:
P
Case (1): If (x) is an n-th degree polynomial, then write yp = nj=0 Aj xj . He
Math 3D: Differential Equations
Midterm (44520)
Oct 28th, 2016
14:0014:50
Name:
Student Id#:
Discussion Class Time:
Total marks = 50 (per question in brackets)
No calculators or other electronic devices
Unless otherwise stated, include all your working fo
Math 3D Differential Equations Extra Questions for Midterm Prep
Nothing for submission
1. Three independent solutions are given to the following differential equation. Find the solution
satisfying the given initial conditions.
y000 3y00 + 4y0 2y = 0,
y1 =
Math 3D Differential Equations Homework Questions 2
Submit the * questions on Thursday of Week 3 (Jan 26th)
15 Find the general solution of the differential equation. If an initial condition is given, find the
corresponding particular solution.
1. y0 + 3y
Ch 2.3 and 2.5 Worksheet - Math 3D Feb. 7th
Aaron Chen
Chapter 2.3 - Higher Order Linear ODEs
Summary: Still assume y = erx and solve for r. Now there can be higher multiplicities, where we
multiply by respective powers of x. We thus have to know linear i
Math 3D Book Solutions 4
3.3
Linear Systems of ODES
1
2
2 3t
sin t
= P(t)x + f(t) ! = t
x+
e
3
cos t
1 3
1 4t
4 4t
1 4t
1 4t
d
e =
e =4
e = dt
(a)
e
3 1
1
4
1
1
1 3
1
2 2t
1
e2t =
e
= 2
e2t =
3 1
1
2
1
x0
x0
d
dt
1
e2t
1
(b) The general solu
Name
Physics 2
Week 3 Quiz
October 14, 2016
Student ID
Problem 1 (4 points)
You are on the roof of a 10 m tall building. You throw a ball downward from the
rooftop with an initial speed of 1.0 m/s. The ball bounces off the ground and when
traveling upward
1. Electric Forces and Fields (8 pts)
a. Positive charges q = +4.00 C are placed at 5 of the 6 corners of a regular hexagon,
as shown. The distance from each corner of the hexagon to the center is 12.0 cm.
Find the magnitude and direction of the electric