Question 1: Consider a block of mass m attached to a spring with force constant k, as shown in the figure. The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x =0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. k how m

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Chapter1: Units, Trigonometry. And Vectors
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Question 1:
Consider a block of mass m attached to a spring with force
constant k, as shown in the figure. The spring can be either
stretched or compressed. The block slides on a frictionless
horizontal surface, as shown. When the spring is relaxed, the
block is located at x =0. If the block is pulled to the right a
distance A and then released, A will be the amplitude of the
resulting oscillations.
Assume that the mechanical energy of the block-spring
system remains unchanged in the subsequent motion of the
block.
wwwwwwwww
-A
0
a) After the block is released from x = A, it will:
remain at rest.
move to the left until it reaches equilibrium and
stop there.
move to the left until it reaches x = -A and stop
there.
a.
b.
C.
move to the left until it reaches x = -A and then
begin to move to the right.
The time it takes the block to complete one cycle is called the
period. Usually, the period is denoted T and is measured in
seconds.
R
0
m
d.
The frequency, denoted f, is the number of cycles that are
completed per unit of time: f= 1/T. In SI units, fis measured
in inverse seconds, or hertz (Hz).
b) If the period is doubled, the frequency is:
unchanged.
Q
A
a.
b. doubled.
halved.
C.
c) An oscillating object takes 0.10 s to complete one cycle;
that is, its period is 0.10 s. What is its frequency f?
d) If the frequency is 40 Hz, what is the period T?
The following questions refer to the second figure below that
graphically depicts the oscillations of the block on the spring.
Note that the vertical axis represents the x coordinate of the
oscillating object, and the horizontal axis represents time.
K L M
NA
e) Which points on the x axis are located a distance A from
the equilibrium position?
a.
R only.
b. Qonly.
C.
both R and Q.
f) Suppose that the period is T. Which of the following
points on the taxis are separated by the time interval T?
K and L.
K and M.
K and P.
L and N.
e.
M and P.
Now assume for the remaining Parts g) - j), that the x
coordinate of point R is 0.12 m and the t coordinate of point K
is 0.0050 s.
g) What is the period T?
i)
Hint: In moving from the point t = 0 to the point K, what
fraction of a full wavelength is covered? Call that fraction
a. Then you can set aT = 0.005s. Dividing by the fraction a
will give the period T.
h) How much time t does the block take to travel from the
point of maximum displacement to the opposite point of
maximum displacement?
What distance d does the object cover during one period
of oscillation?
j)
A
a.
b.
C.
d.
Question 2:
Consider a harmonic oscillator at four different moments,
labeled A, B, C, and D, as shown in the figure below. Assume
that the force constant k, the mass of the block, m, and the
amplitude of vibrations, A, are given. Answer the following
questions.
-A-A-2²
B
C
D
What distance d does the object cover between the
moments labeled K and N on the graph?
การแบบน
k
0 A/2 A
www
m
m
m
a) Which moment corresponds to the maximum potential
energy of the system?
b) Which moment corresponds to the minimum kinetic
energy of the system?
Transcribed Image Text:Question 1: Consider a block of mass m attached to a spring with force constant k, as shown in the figure. The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x =0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. wwwwwwwww -A 0 a) After the block is released from x = A, it will: remain at rest. move to the left until it reaches equilibrium and stop there. move to the left until it reaches x = -A and stop there. a. b. C. move to the left until it reaches x = -A and then begin to move to the right. The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds. R 0 m d. The frequency, denoted f, is the number of cycles that are completed per unit of time: f= 1/T. In SI units, fis measured in inverse seconds, or hertz (Hz). b) If the period is doubled, the frequency is: unchanged. Q A a. b. doubled. halved. C. c) An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequency f? d) If the frequency is 40 Hz, what is the period T? The following questions refer to the second figure below that graphically depicts the oscillations of the block on the spring. Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time. K L M NA e) Which points on the x axis are located a distance A from the equilibrium position? a. R only. b. Qonly. C. both R and Q. f) Suppose that the period is T. Which of the following points on the taxis are separated by the time interval T? K and L. K and M. K and P. L and N. e. M and P. Now assume for the remaining Parts g) - j), that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s. g) What is the period T? i) Hint: In moving from the point t = 0 to the point K, what fraction of a full wavelength is covered? Call that fraction a. Then you can set aT = 0.005s. Dividing by the fraction a will give the period T. h) How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? What distance d does the object cover during one period of oscillation? j) A a. b. C. d. Question 2: Consider a harmonic oscillator at four different moments, labeled A, B, C, and D, as shown in the figure below. Assume that the force constant k, the mass of the block, m, and the amplitude of vibrations, A, are given. Answer the following questions. -A-A-2² B C D What distance d does the object cover between the moments labeled K and N on the graph? การแบบน k 0 A/2 A www m m m a) Which moment corresponds to the maximum potential energy of the system? b) Which moment corresponds to the minimum kinetic energy of the system?
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