9-7 Simple Harmonic Motion versus Uniform Circular Motion Simple harmonic motion is equivalent to the projection of uniform circular motion along the x axis. Assume an object moves in a 1.0 m-radius circle with a constant angular velocity of o = /4 radians per second. How long will it take to complete one cycle? _8Cs] UCM SHM 1+x +x +Xo- 0. - Xo- Record the object's angular displacement, 0, at each time, t, listed below. Mark its location on the circle and on the x axis below. Then calculate the x coordinate of the object and plot t as a function of time. (Hint: Use the sine function) t (s) 1 3 4 6 7 8. e (radians) 31 דר x (m) 0.7 0.7 -1 -0.7 -0.7 0. 1.0 m X Om t (s) 1 2 4 5. 6. -1.0 m
9-7 Simple Harmonic Motion versus Uniform Circular Motion Simple harmonic motion is equivalent to the projection of uniform circular motion along the x axis. Assume an object moves in a 1.0 m-radius circle with a constant angular velocity of o = /4 radians per second. How long will it take to complete one cycle? _8Cs] UCM SHM 1+x +x +Xo- 0. - Xo- Record the object's angular displacement, 0, at each time, t, listed below. Mark its location on the circle and on the x axis below. Then calculate the x coordinate of the object and plot t as a function of time. (Hint: Use the sine function) t (s) 1 3 4 6 7 8. e (radians) 31 דר x (m) 0.7 0.7 -1 -0.7 -0.7 0. 1.0 m X Om t (s) 1 2 4 5. 6. -1.0 m
Related questions
Question
I have don’t the first page. Please help with the second page. The second page had relations to the first page so I added both. Thank you!
Transcribed Image Text:9-7
Questions:
1. Describe the graph of displacement versus time created on the preceding page:
2. Write an equation for x(t) in terms of w :
3. Assume instead that the object moves in a 2.0 m-radius circle with a constant angular
velocity of o = x/2 radians per second.
a) How long will it take to complete one cycle?
b) Make a rough sketch of the x coordinate of the object as a function of time.
20 m
X
Om
t (s)
3.
6
8
-2.0 m
c) Write an equation for x(t) in terms of o:
4) Assume the object graphed in question 3 is moving in simple harmonic motion.
a) What is the frequency the motion, f?
b) Write an equation for the relationship between angular velocity, w, and frequency, f.
c) Write an equation for the relationship between angular velocity, w, and period T.
![9-7 Simple Harmonic Motion versus Uniform Circular Motion
Simple harmonic motion is equivalent to the projection of uniform circular motion along
the x axis. Assume an object moves in a 1.0 m-radius circle with a constant angular velocity
of w = x/4 radians per second. How long will it take to complete one cycle? _8Cs]
UCM
SHM
1+x
+x
+ Xo-
of dh
- Xo-
rad
r: 1 Cm]
Record the object's angular displacement, 0, at each time, t, listed below. Mark its location
on the circle and on the x axis below. Then calculate the x coordinate of the object and plot
it as a function of time. (Hint: Use the sine function)
t (s)
1
2
3
4
7
8
e (radians)
T/4
3 tr
דר
4
x (m)
0.7
1.
0.7
- 1
-0.7
-0.7
1.0 m
X 0m
t (s)
1
2.
4.
5.
-1.0 m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F556f2d2a-567a-4c31-b94a-128a2a7d7031%2F0a8a1d26-aae3-4401-ab08-7bc0001f06e3%2Fbkeiml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9-7 Simple Harmonic Motion versus Uniform Circular Motion
Simple harmonic motion is equivalent to the projection of uniform circular motion along
the x axis. Assume an object moves in a 1.0 m-radius circle with a constant angular velocity
of w = x/4 radians per second. How long will it take to complete one cycle? _8Cs]
UCM
SHM
1+x
+x
+ Xo-
of dh
- Xo-
rad
r: 1 Cm]
Record the object's angular displacement, 0, at each time, t, listed below. Mark its location
on the circle and on the x axis below. Then calculate the x coordinate of the object and plot
it as a function of time. (Hint: Use the sine function)
t (s)
1
2
3
4
7
8
e (radians)
T/4
3 tr
דר
4
x (m)
0.7
1.
0.7
- 1
-0.7
-0.7
1.0 m
X 0m
t (s)
1
2.
4.
5.
-1.0 m
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
