February 08, 2013
1
A mass attached to a spring oscillates back and forth as indicated
in the position vs. time plot below. At point P, the mass has
A
B
positive velocity and positive acceleration.
positive velocity and negative acceleration.
C
positive velocity and zero acceleration.
D
negative velocity and positive acceleration.
E
negative velocity and negative acceleration.
F
negative velocity and zero acceleration.
G
zero velocity but is accelerating (positively or negatively).
February 08, 2013
2
A mass suspended from a spring is oscillating up and down as indicated.
Consider two possibilities:
(i) at some point during the oscillation the mass has zero
velocity but is accelerating (positively or negatively);
(ii) at some point during the oscillation the mass has zero
velocity and zero acceleration.
A
B
C
D
Both occur sometime during the oscillation.
Neither occurs during the oscillation.
Only (i) occurs.
Only (ii) occurs.
February 08, 2013
3
An object hangs on a spring and bounces up and down. The
potential energy is graphed below. Consider point O. The
position at this point must be
A
either an upper or a lower extreme: there's no way to know.
B
an upper extreme
C
a lower extreme
D
a mid point
O
February 08, 2013
4
A single person swings on a swing without pumping, so the swing
oscillates back and forth at its natural frequency. If, instead, two
people sit on the swing, the natural frequency
of the swing is
A
greater.
B
the same.
C smaller.
February 08, 2013
5
A person swings on a swing without pumping, so the swing
oscillates back and forth at its natural frequency. If, instead, the
person stands on the swing (again, no pumping), the natural
frequency of the swing is
A
greater.
B
the same.
C smaller.
February 08, 2013
6 A string is clamped at both ends and plucked so it vibrates in a standing mode
as shown below. How many nodes and antinodes are there?
A
2 nodes, 3 antinodes
B
3 nodes, 2 antinodes
C 4 nodes, 3 antinodes
D 3 nodes, 4 antinodes
February 08, 2013
7 A string is clamped at both ends and plucked so it vibrates in a
standing mode between two extreme positions a and b. Let
upward motion correspond to positive velocities. When
the string is in position c, the instantaneous velocity of points
along the string:
A
is zero everywhere.
B
is positive everywhere.
C is negative everywhere.
D depends on location on the string
Explanation on next page
February 08, 2013
Answer: D: Depends on location.
The drawing below shows the string just
before (top) and just after (bottom) it
reaches position c (middle). Notice that dot
P moves down and dot R moves up,
whereas dot Q doesn’t move at all. So the
velocities of points around dot P are
negative and those of points around dot R
are positive. Dot Q doesn’t move and has
zero velocity at all times.
February 08, 2013
8
At what point will the pendulum bob have maximum positive velocity?
(Let right be positive and left be negative.)
A
Point A
B
Point B
C
Point C
D
Point D
February 08, 2013
9
At what point will the pendulum bob have maximum positive acceleration?
(Let right be positive and left be negative.)
A
Point A
B
Point B
C
Point C
D
Point D
February 08, 2013
10
Below is a graph of the x-component of the weight as a function of time.
Which point (ABCD) corresponds to the X on the graph?
(Let right be positive and left be negative.)
A
Point A
B
Point B
C
Point C
D
Point D
t
Fgx
X
February 08, 2013
11
A vibrating string creates a standing wave, as shown below. If the string is 2
meters long, find the wavelength.
A
2 meters
B
1.5 meters
C 0.8 meters
D 0.5 meters
E
0.4 meters
February 08, 2013
12 By shaking one end of a stretched string, a single pulse
is generated. The traveling pulse carries
A energy and momentum
B energy
C momentum
D neither of the two
February 08, 2013
13 Suppose you are given an acceleration-vs-time graph for
a pendulum system. Which of the following could you
determine? (Mark all that apply.)
A T: period of oscillation
a
B L: length of pendulum
C m: mass of pendulum bob
Explanation on next page
February 08, 2013
Suppose you are given an acceleration-vs-time graph for a
pendulum system. Which of the following could you
determine? (Mark all that apply.)
A T: period of oscillation
difference of time values for
two crests or two troughs
B L: length of pendulum
C m: mass of pendulum bob
a
The way a pendulum swings is
independent of the bob's mass.
February 08, 2013
14 Suppose you are given a x-vs-t graph and a F-vs-t graph for a
mass-on-a-spring system. Which of the following can you
determine? (Mark all that apply.)
A T: difference of time
values for two crests or
two troughs
x
B k: compare points on
two graphs: F = -kΔx
C m: use the above and
D a: take any point on the
F-graph and divide by m:
F
February 08, 2013
15 Suppose you are given an a-vs-t graph and a F-vs-t graph for a
mass-on-a-spring system. Which of the following can you
determine? (Mark all that apply.)
A T: difference of time
values for two crests or
two troughs
a
B m: compare points on
two graphs: F = ma
C k: use the above and
D x: take any point on the
F-graph and divide by k:
F