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| 183_notes:springmotion [2021/02/18 21:04] – [Model of a Spring] stumptyl | 183_notes:springmotion [2024/01/31 17:07] (current) – caballero |
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| {{url>http://www.pa.msu.edu/~caballero/teaching/simulations/HorizontalSpring.html 675px,425px|Mass on a Spring}} | {{url>https://glowscript.org/#/user/danny/folder/Shared/program/HorizontalSpring 700px,525px|Mass on a Spring}} |
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| {{url>https://plot.ly/~dannycab/12/640/480 640px,480px|Plot of spring-mass system}} | {{url>https://glowscript.org/#/user/danny/folder/Shared/program/SpringMassGraphs 700px,300px|Plot of spring-mass system}} |
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| You might have seen this kind of plot before. It's a [[http://en.wikipedia.org/wiki/Sine_wave|sinusoidal function]], in this case it's a sine curve. So the formula that describes this function could be something like: | You might have seen this kind of plot before. It's a [[http://en.wikipedia.org/wiki/Sine_wave|sinusoidal function]], in this case it's a sine curve. So the formula that describes this function could be something like: |
| $$\omega = \dfrac{2\pi}{T}$$ | $$\omega = \dfrac{2\pi}{T}$$ |
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| where $\omega$ is the rate of oscillation in terms of how many radians the spring-mass system moves through each second. | __//where $\omega$ is the rate of oscillation in terms of how many radians the spring-mass system moves through each second (rad/s). |
| | //__ |
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| [[http://en.wikipedia.org/wiki/Robert_Hooke|Robert Hooke]] investigated this type of motion in the mid 1600s((As it turns out, Hooke was also a great biologist, astronomer, paleontologist, and mathematician. It's amazing what you can do when TV hasn't been invented.)). He found that the interaction (force) that gave rise to this motion was one that increased linearly with the displacement of the object (stretch or compression of the spring) and that was directed opposite the direction of this displacement. In other words, if you stretch a spring (by pulling it), it will pull back on you. If you compress it (by pushing it), it will push back on you. Moreover, these two forces will be equal in size if the stretch and compression are of the same size. | [[http://en.wikipedia.org/wiki/Robert_Hooke|Robert Hooke]] investigated this type of motion in the mid 1600s((As it turns out, Hooke was also a great biologist, astronomer, paleontologist, and mathematician. It's amazing what you can do when TV hasn't been invented.)). He found that the interaction (force) that gave rise to this motion was one that increased linearly with the displacement of the object (stretch or compression of the spring) and that was directed opposite the direction of this displacement. In other words, if you stretch a spring (by pulling it), it will pull back on you. If you compress it (by pushing it), it will push back on you. Moreover, these two forces will be equal in size if the stretch and compression are of the same size. |