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1.5 Example of investigate the motion of an oscillator using experimental and graphical methods
1.5.1.Q1: what is the maximum angle of release before the motion is not accurately described as a simple harmonic motion for the case of a simple free pendulum?
Example 1: Simple pendulum A pendulum bob given an initial horizontal displacement and released to swing freely to produce to and fro motion
1.5.2 Suggested Inquiry Steps:
- Define the question in your own words
- Plan an investigation to explore angle of release to record the actual period T and theoretical period where L is the length of the mass pendulum of mass, m and g is the gravitational acceleration of which the mass is experiencing, on Earth's surface g = 9.81 m/s2
- A suggested record of the results could look like this
angle / degree | T /s | Ttheory / s | |
05 | |||
10 | |||
15 | |||
20 | |||
30 | |||
40 | |||
50 | |||
60 | |||
70 | |||
80 | |||
90 |
With the evidences collected or otherwise, suggests what the conditions of which the angle of oscillation can the actual period T be approximated to theoretical period such that T ≈
1.5.3 Suggested Answer 1:
angle θ ≈ 10 degrees for , depending on what is the error acceptable, small angle is typically about less than 10 degree of swing from the vertical.
1.5.4 Conclusion:
Motion approximates simple harmonic motion when the angle of oscillation is small < 10 degrees..
1.5.5 Other Interesting fact(s):
Motion approximates SHM when the spring does not exceed limit of proportionality during oscillations.
1.5.6 Real Life Application of Small Angle Approximations:
Astronomical applications of the Small Angle Approximation
1.5.7 YouTube
http://youtu.be/BRbCW2MsL94?t=2m16s This video shows many pendulums that goes in phase and out of phase with each other pendulum to creating a visually stunning effect.
1.5.8 Model:
Translations
Code | Language | Translator | Run | |
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Credits
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Apps
https://play.google.com/store/apps/details?id=com.ionicframework.shm195app415781&hl=en
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- Details
- Parent Category: 02 Newtonian Mechanics
- Category: 09 Oscillations
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