LO Problem

Pendulums of America

The Mission

Pendulums of America has asked you specifically to create the next big creation.

Their designers stated that they want a pendulum that swings every second, that the bob will be made out of steel.

Source: http://www.cobbcocorporate.com.au/personalisation.html

In order to solve this problem we need to assume two things

The resistance of air is negligible

All of the mass of the pendulum is in the bob

Now lets do some physics

Find the length of the pendulum

T =1

T = 1

T=2\pi\sqrt {L \over g}

T = 2 π \sqrt ​ \frac{​ L ​ ​}{​ g ​} ​ ​ ​

L={T^2g \over {(2 \pi)}^2}

L = \frac{​ T ​ 2 ​ ​ g ​ ​}{​ ( 2 π ) ​ 2 ​ ​ ​}

L= {{(1)}^2 \times 9.81 \over ({2 \pi})^2}

L = \frac{​ ( 1 ) ​ 2 ​ ​ \times 9 . 8 1 ​ ​}{​ ( 2 π ) ​ 2 ​ ​ ​}

L= 0.248 m

L = 0.248 m

Now lets do some physics

We can find the length of the pendulum easily if we use the formula that appears in step 2.

Faaaaasssstttt

Find the angular speed of the pendulum

Faaaaasssstttt

Find the angular speed of the pendulum

\omega = \sqrt{g \over L}

ω = \sqrt ​ \frac{​ g ​ ​}{​ L ​} ​ ​ ​

\omega = \sqrt 9

ω = \sqrt ​ 9 ​ ​ ​

Conclusion

Use SHM is really easy when it comes to pendulums, it is easy to use and can be used in everyday life. For example, measurement of a pendulum length.

This can help us predict how a pendulum will behave depending on its length and we can calibrate really precise things such as clocks because we understand how pendulums swing.