12. Which position or positions? B Has maximum velocity? B. SMaximum + force? Acceleration = 0? Maximum kinetic energy? No potential clastic energy? X is a negative maximum? Zero amplitude. wwwwA A. C. [wwwB D. E. F. G.
12. Which position or positions? B Has maximum velocity? B. SMaximum + force? Acceleration = 0? Maximum kinetic energy? No potential clastic energy? X is a negative maximum? Zero amplitude. wwwwA A. C. [wwwB D. E. F. G.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
Question 12
![Spring-Mass Systems
Harmonic Motion Basics -
Spring Constant (k in N/m) – The spring constant tells you
how strong (stiff) a spring is. A stiffer spring has a bigger k.
Amplitude (A) - maximum displacement from the
equilibrium position. The amount of energy
in a spring-mass system is determined ONLY
y the amplitude.
Period (T)- time for one complete cycle.
Frequency (f) - number of cycles in one second.
Amplitude - 14 cm
Period (T) = 4.2 sec
k-
k=
0:00.0
start
20 N/m
20 N/m
k = 20 N/m
..
faster T
k-
faster T
M MM M
10 N/m
20 N/m
0:04.2
stop
With the same spring constant
more mass causes a slower
vibration (larger T).
With the same mass the
stronger spring (bigger k) will
vibrate faster (maller T).
28 cm
A spring-mass system is called Simple Harmonic Motion (SHM)
because the force is directly proportional to the displacement of
the spring. Anything that follows this rule is known as Simple
Harmonic Motion. (A pendulum is only close to simple harmonic
motion.)
Hooke's Law:
Spring Constant (in N/m):
bigger k= stiffer spring.
Force (in N)
of the
spring
»F=-kx
displacement (in m) from
the equilibrium position.
Equilibrium position (where it will come
to rest; where it was before disturbed)
The restoring force
(F) tries to return it
to its equilibrium
position.
Force and Position: As seen above in Hooke's Law
F and x always oppose each other. If F is positive, x is
negative, etc. [k, though, is always positive]).
Stretched
wwww
X-+A; F=-max
Stretched Spring–The spring gets bigger,
so x is positive and F is negative.
Compressed Spring-The spring gets smaller,
so x is negative and F is positive.
At equilibrium: Regardless if it is moving or not, at
the equilibrium position the spring does not apply
a force. x=0 and F=0.
M
a--max; v -0
PE = max; KE =0
Relaxed
[www
x = 0; F =0
a = 0; v=-max
PE = 0; KE = max
M
Acceleration (a), Velocity (v), and Energy (E)
It should be obvious that where the force is zero
(equilibrium position), the acceleration is zero.
At the ends the mass stops for an instant, so v=0
and KE - 0, but PE is a maximum (PE- Vlox).
The mass speeds up as it moves toward the center,
where it has maximum v and KE and minimum PE,
Compressed
x=-A; F= +max
a =+max; v= 0
PE = max; KE = 0
+F
Period of a Spring-Mass System:
Ex. A 350 g mass is attached to a spring that has
a spring constant of 12 N/m. What is the period of
vibration?
Notice that amplitude
is not in the equation.
Just as in all harmonic
motion-amplitude
does not affect the
period or frequency of
a spring-mass system.
Period
Mass
(in sec)
(in kg)
m
T = 2n,
Variables:
m = 0.35 kg
(1000 g =1 kg)
k= 12 N/m
T = 2x.
Spring
constant
(in N/m)
T= 6.28.0292
k
T= 6.28(.1709)
35
T =1.07 seç
T = 6.2812
T =
cstephenmurray.com
Copyright © 2013, C. Stephen Murray
wwwwwwww
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Transcribed Image Text:Spring-Mass Systems
Harmonic Motion Basics -
Spring Constant (k in N/m) – The spring constant tells you
how strong (stiff) a spring is. A stiffer spring has a bigger k.
Amplitude (A) - maximum displacement from the
equilibrium position. The amount of energy
in a spring-mass system is determined ONLY
y the amplitude.
Period (T)- time for one complete cycle.
Frequency (f) - number of cycles in one second.
Amplitude - 14 cm
Period (T) = 4.2 sec
k-
k=
0:00.0
start
20 N/m
20 N/m
k = 20 N/m
..
faster T
k-
faster T
M MM M
10 N/m
20 N/m
0:04.2
stop
With the same spring constant
more mass causes a slower
vibration (larger T).
With the same mass the
stronger spring (bigger k) will
vibrate faster (maller T).
28 cm
A spring-mass system is called Simple Harmonic Motion (SHM)
because the force is directly proportional to the displacement of
the spring. Anything that follows this rule is known as Simple
Harmonic Motion. (A pendulum is only close to simple harmonic
motion.)
Hooke's Law:
Spring Constant (in N/m):
bigger k= stiffer spring.
Force (in N)
of the
spring
»F=-kx
displacement (in m) from
the equilibrium position.
Equilibrium position (where it will come
to rest; where it was before disturbed)
The restoring force
(F) tries to return it
to its equilibrium
position.
Force and Position: As seen above in Hooke's Law
F and x always oppose each other. If F is positive, x is
negative, etc. [k, though, is always positive]).
Stretched
wwww
X-+A; F=-max
Stretched Spring–The spring gets bigger,
so x is positive and F is negative.
Compressed Spring-The spring gets smaller,
so x is negative and F is positive.
At equilibrium: Regardless if it is moving or not, at
the equilibrium position the spring does not apply
a force. x=0 and F=0.
M
a--max; v -0
PE = max; KE =0
Relaxed
[www
x = 0; F =0
a = 0; v=-max
PE = 0; KE = max
M
Acceleration (a), Velocity (v), and Energy (E)
It should be obvious that where the force is zero
(equilibrium position), the acceleration is zero.
At the ends the mass stops for an instant, so v=0
and KE - 0, but PE is a maximum (PE- Vlox).
The mass speeds up as it moves toward the center,
where it has maximum v and KE and minimum PE,
Compressed
x=-A; F= +max
a =+max; v= 0
PE = max; KE = 0
+F
Period of a Spring-Mass System:
Ex. A 350 g mass is attached to a spring that has
a spring constant of 12 N/m. What is the period of
vibration?
Notice that amplitude
is not in the equation.
Just as in all harmonic
motion-amplitude
does not affect the
period or frequency of
a spring-mass system.
Period
Mass
(in sec)
(in kg)
m
T = 2n,
Variables:
m = 0.35 kg
(1000 g =1 kg)
k= 12 N/m
T = 2x.
Spring
constant
(in N/m)
T= 6.28.0292
k
T= 6.28(.1709)
35
T =1.07 seç
T = 6.2812
T =
cstephenmurray.com
Copyright © 2013, C. Stephen Murray
wwwwwwww
wwwwwwmD
Transcribed Image Text:12.
Spring-Mass Systems p.2
4. Two different masses are suspended
from springs with the same spring
constant, which will have the faster
period?
1.
Which of the springs has the
bigger spring constant?
1Right
2. How do you know for certain?
200 8
Not as streached
5. Why?
200
g
3. Which will vibrate faster?
400 g
tether th
O200 g
k = 20 N/m
k= 20 N/m
k= 10 N/m
k = 10 N/m
B. 2M MM2M
M WM
C.
M W M
D.
2M W 2M
A.
L20 cm
L20 em
L20 cm -
20 cm-
0:00.0
0:01.6
10
What is the amplitude of spring A?
10. What is the period of spring D2
6.
1.6xZ =13.25
7. What is the amplitude of spring B?
11. Find the mass on spring D.
8.
A or B will have the fastest period?
9.
A or C will have the slowest period?
18. Find the period of a spring mass system that has a 5.4 kg
mass and a 60 N/m spring constant.
12. Which position or positions?
A. 13 Has maximum velocity?
B. SMaximum + force?
Acceleration = 0?
Maximum kinetic energy?
No potential elastic energy?
X is a negative maximum?
Zero amplitude.
wwwA
[wwwB
C.
D.
Е.
F.
G.
13. Positive or negative displacement (x).
A. -
B. ŁA stretched spring (the spring is longer)
C. 1 Pulling on a spring so it stretches.
D. Pushing on a spring so that it compresses.
E.
Position vs. Time
A compressed spring (the spring gets shorter)
t Hanging a mass on a spring.
14. In F=-kx, is F the spring or what's pulling on the spring?
15. If I pull on a spring with 20 N, then the spring pulls back
with how much force?
Time (sec)
16. A 5 kg object stretches a spring 20 cm.
A. How much force is pulling on the spring ?
19. What is the amplitude of the above graph?
B. Find the spring constant.
20. What is the period of the above graph?
21. If it has a 3 kg mass on it, what is its spring constant?
17. A 300 g mass stretches a spring 50 cm, find the spring
constant.
Copyright © 2013, C. Stephen Murray
cstephenmurray.com
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