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It seems the homework tag applies even if it is not actual homework
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Qmechanic ♦
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I am investigating the period of a pendulumpendulum swing. This is a simple harmonic pendulum and I am already aware of the common, but slightly inaccurate, $2\pi \sqrt{\frac{L}{G}}$ formula.

My problem is that I cannot figure out how to find the total distance traveled by the bob since the angle between $F_{g}$ and the string is constantly changing as the bob falls and therefore the acceleration is not constant.

Question: So, my question is, how do I calculate the distance when the acceleration is not constant?

Notes:

  • $F_{g}$ is the force of gravity pulling the bob downward.

  • $\sin\theta$ is the tangential force of the pendulum and it represents the force applied to the bob causing a the swing. It is the projection of $F_{g}$ onto the string.

  • $\theta$ is the angle between $F_{g}$ and the string

  • The movement of this bob is being considered as falling being dropped from 0 degrees (with respect to the unit circle) and continuing until it reaches a distance of $\frac{r*\pi}{2}$ where $r$ is the length of the string and the radius of the circular path.

  • The distance formula used is $d=v_{1}*t + \frac{1}{2}*a*t^{2}$ but since the initial velocity is 0 it is not being considered. I also believe this formula to be inaccurate since the acceleration is not constant.

Diagram: My Considerations

I am investigating the period of a pendulum swing. This is a simple harmonic pendulum and I am already aware of the common, but slightly inaccurate, $2\pi \sqrt{\frac{L}{G}}$ formula.

My problem is that I cannot figure out how to find the total distance traveled by the bob since the angle between $F_{g}$ and the string is constantly changing as the bob falls and therefore the acceleration is not constant.

Question: So, my question is, how do I calculate the distance when the acceleration is not constant?

Notes:

  • $F_{g}$ is the force of gravity pulling the bob downward.

  • $\sin\theta$ is the tangential force of the pendulum and it represents the force applied to the bob causing a the swing. It is the projection of $F_{g}$ onto the string.

  • $\theta$ is the angle between $F_{g}$ and the string

  • The movement of this bob is being considered as falling being dropped from 0 degrees (with respect to the unit circle) and continuing until it reaches a distance of $\frac{r*\pi}{2}$ where $r$ is the length of the string and the radius of the circular path.

  • The distance formula used is $d=v_{1}*t + \frac{1}{2}*a*t^{2}$ but since the initial velocity is 0 it is not being considered. I also believe this formula to be inaccurate since the acceleration is not constant.

Diagram: My Considerations

I am investigating the period of a pendulum swing. This is a simple harmonic pendulum and I am already aware of the common, but slightly inaccurate, $2\pi \sqrt{\frac{L}{G}}$ formula.

My problem is that I cannot figure out how to find the total distance traveled by the bob since the angle between $F_{g}$ and the string is constantly changing as the bob falls and therefore the acceleration is not constant.

Question: So, my question is, how do I calculate the distance when the acceleration is not constant?

Notes:

  • $F_{g}$ is the force of gravity pulling the bob downward.

  • $\sin\theta$ is the tangential force of the pendulum and it represents the force applied to the bob causing a the swing. It is the projection of $F_{g}$ onto the string.

  • $\theta$ is the angle between $F_{g}$ and the string

  • The movement of this bob is being considered as falling being dropped from 0 degrees (with respect to the unit circle) and continuing until it reaches a distance of $\frac{r*\pi}{2}$ where $r$ is the length of the string and the radius of the circular path.

  • The distance formula used is $d=v_{1}*t + \frac{1}{2}*a*t^{2}$ but since the initial velocity is 0 it is not being considered. I also believe this formula to be inaccurate since the acceleration is not constant.

Diagram: My Considerations

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Investigation of a pendulum's period, problem creating equation to sum the dynamic velocity

I am investigating the period of a pendulum swing. This is a simple harmonic pendulum and I am already aware of the common, but slightly inaccurate, $2\pi \sqrt{\frac{L}{G}}$ formula.

My problem is that I cannot figure out how to find the total distance traveled by the bob since the angle between $F_{g}$ and the string is constantly changing as the bob falls and therefore the acceleration is not constant.

Question: So, my question is, how do I calculate the distance when the acceleration is not constant?

Notes:

  • $F_{g}$ is the force of gravity pulling the bob downward.

  • $\sin\theta$ is the tangential force of the pendulum and it represents the force applied to the bob causing a the swing. It is the projection of $F_{g}$ onto the string.

  • $\theta$ is the angle between $F_{g}$ and the string

  • The movement of this bob is being considered as falling being dropped from 0 degrees (with respect to the unit circle) and continuing until it reaches a distance of $\frac{r*\pi}{2}$ where $r$ is the length of the string and the radius of the circular path.

  • The distance formula used is $d=v_{1}*t + \frac{1}{2}*a*t^{2}$ but since the initial velocity is 0 it is not being considered. I also believe this formula to be inaccurate since the acceleration is not constant.

Diagram: My Considerations