Consider the oscillation of a mass-spring system, where x = A cos(wt + ø). At the time t = 0, the mass is at x = 0 and it is moving to the right with a speed vo. - vo k ele m x = 0 Find the phase angle ø. Consider x as the projection of a counter-clockwise uniform circular motion.

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter3: Oscillations
Section: Chapter Questions
Problem 3.22P: Let the initial position and speed of an overdamped, nondriven oscillator be x0 and v0,...
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a) phase angle (image attached)

1) pi

2) 0

3) pi/4

4) 5pi/4

5) pi/3

6) pi/2

7) 7pi/4

8) 3pi/2

9) 3pi/4

10) 2pi

 

b) image

 

Consider the oscillation of a mass-spring
system, where
x = A cos(wt + ¢).
At the time t = 0, the mass is at x = 0 and it
is moving to the right with a speed vo.
- V0 →
k
m
x = 0
Find the phase angle ø. Consider x as
the projection of a counter-clockwise uniform
circular motion.
Transcribed Image Text:Consider the oscillation of a mass-spring system, where x = A cos(wt + ¢). At the time t = 0, the mass is at x = 0 and it is moving to the right with a speed vo. - V0 → k m x = 0 Find the phase angle ø. Consider x as the projection of a counter-clockwise uniform circular motion.
Find the total energy of the oscillation at
T
t =
where T is the period.
8°
1
m võ
4
1. Е
2. E = 3 m vó
3
3. Е
m
2
4. E = 4m vő
3
5. Е
m vố
4
1
m vổ
6. Е
7. Е — т
5
8. Е —
m vố
m
9. E
m vố
10. E
2 m vở
IN
||
||
Transcribed Image Text:Find the total energy of the oscillation at T t = where T is the period. 8° 1 m võ 4 1. Е 2. E = 3 m vó 3 3. Е m 2 4. E = 4m vő 3 5. Е m vố 4 1 m vổ 6. Е 7. Е — т 5 8. Е — m vố m 9. E m vố 10. E 2 m vở IN || ||
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