1
Winter 2011
Physics 6B
Katsushi Arisaka
Sample Exam for the First Midterm
Important Remarks:
•
The First Midterm Exam is on Monday, January 24 in class.
•
Closed book, closed note, no calculator is allowed at the exam.
•
You are not allowed to bring any sheet of paper with equations (i.e. a cheating sheet not
allowed).
•
The real exam will be similar to this sample, but
much shorter
!
•
Two review sessions are tentatively scheduled on
o
Thursday, January 20 at 24 pm.
o
Thursday, January 20 at 68 pm.
(Location to be announced later.) Some of the difficult questions in this sample exam will be
reviewed.
How to prepare for exams:
•
Try to solve this sample exam without opening the textbook or notebook first. (It is however
not wise to spend too much time for the first time.)
•
If you cannot solve quickly, read the lecture note or the textbook where the solution is given.
Once you recognize the solution, close the textbook and notebook, then write the answer on a
white piece of paper.
•
Do not simply copy the solution from the textbook/notebook. You’d better spend enough time
until you full understand the concept.
•
If you can not grasp the solution quickly, you are missing some important concept in physics.
Read the textbook and notebook of relevant chapters carefully.
•
Often you can not solve the problems because your background knowledge/preparation in
Mathematics is weak. If this is the case, at least, review the math by reading the Appendix of
the Textbook.
•
Try to finish by the review session on Thursday, January 20.
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2
1.
Let’s explore a simple massspring system. A mass (
m
) is connected to a spring (with spring
constant
k
) as shown below. There is no friction on the floor. At
t
= 0, the mass is slowly
displaced to the left to
x = A
, then released.
a.
Write down the Hooke’s law and Newton’s law which describe this system when the mass
is located at position
x
.
b.
By combining both together, derive the secondorder differential equation (in time) for the
position
x
.
c.
Assume that the solution is given by
cos(
).
x
A
t
ω
=
−
Derive the speed
v
first, then derive
the acceleration
a
next.
d.
Plot the graphs of
x
,
v
and
a
as a function of
t
. Clearly mark the maximum values (on
x
,
v
and
a
) as well as the period
T
.
e.
Show that the assumption
cos(
)
x
A
t
ω
=
−
indeed satisfies the secondorder differential
equation (given at b. above), if the angular frequency
ω
is given by
m
k
=
ω
.
f.
Show that this expression of
ω
has the correct dimension (by applying the “dimensional
analysis” in Textbook Page 810).
g.
Show the relation between Period (
T
), Frequency (
f
) and angular frequency (
ω
). Briefly
describe the physics meaning of each quantity.
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 Spring '10
 GRUNER
 Physics, Energy, Mass, Frequency, Wavelength, secondorder differential equation

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