### About

### 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 $T}_{the\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y}=2\pi \sqrt{\frac{L}{g}$ 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/s
^{2} - A suggested record of the results could look like this

angle / degree | T /s | T_{theory} / s | $err\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}=\frac{(T-{T}_{the\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y})}{T}100\%$ |

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 ≈ $T}_{the\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}y}=2\pi \sqrt{\frac{L}{g}$

### 1.5.3 Suggested Answer 1:

angle θ ≈ 10 degrees for $err\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}=\frac{(2.010-2.006)}{2.010}\left(100\right)=0.2\%$, 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:

### For Teachers

### Translations

Code | Language | Translator | Run | |
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### Software Requirements

Android | iOS | Windows | MacOS | |

with best with | Chrome | Chrome | Chrome | Chrome |

support full-screen? | Yes. Chrome/Opera No. Firefox/ Samsung Internet | Not yet | Yes | Yes |

cannot work on | some mobile browser that don't understand JavaScript such as..... | cannot work on Internet Explorer 9 and below |

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### end faq

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