You built a pendulum clock. How far from the pivot should you place the center of the pendulum mass for a period that is 3.6 secondes

4 years ago

Answered By Jesaiah C

To answer this question we only need to consider the equation for simple harmonice motion. We can describe the Period of a pendulum (T) by the following equation:

$T=2\pi\sqrt{\frac{L}{g}}$T=2π√Lg

L = Length of the pendulum

g = gravitational acceleration (9.81)

All there is to do now is rearrange the equation using algebra, and solve for L. L will be the distance to the pendulum's center of mass from the pivot point.

$L=\frac{T^2g}{4\pi^2}$L=T^{2}g4π^{2}

It is important to note that these equations only work if the angle swept by the pendulum is small (less than 15 degrees). The differential equation that generates this equation can only be linearlized in this range and will not work as well for greater angles.

4 years ago

## Answered By Jesaiah C

To answer this question we only need to consider the equation for simple harmonice motion. We can describe the Period of a pendulum (T) by the following equation:

$T=2\pi\sqrt{\frac{L}{g}}$T=2π√Lg

L = Length of the pendulum

g = gravitational acceleration (9.81)

All there is to do now is rearrange the equation using algebra, and solve for L. L will be the distance to the pendulum's center of mass from the pivot point.

$L=\frac{T^2g}{4\pi^2}$L=T

^{2}g4π^{2}It is important to note that these equations only work if the angle swept by the pendulum is small (less than 15 degrees). The differential equation that generates this equation can only be linearlized in this range and will not work as well for greater angles.

I hope this helps! Good luck!!