I am trying to do a simple pendulum problem but for some reason my answer is different from the book's answer and I don't know what I am doing incorrectly.
The question is:
Consider a simple pendulum that has a length of $50$cm and a maximum horizontal displacement of $8$ cm.
The first portion asks to find the period. So period of a pendulum can be calculated as $T=2\pi \sqrt{\frac{l}{g}}$ where $l$ is the length and $g$ is gravity = $9.81$. Therefore, period of my pendulum should be:
$$\begin{align} &T=2\pi \sqrt{\frac{l}{g}} \\ &T=2\pi \sqrt{\frac{50}{9.81}}\\ &T=14.185 \end{align}$$
But the back of the is suggesting that answer is $T=1.412$s
What am I doing wrong?
Units! The $l=50$ is for 50 cm, but $g=9.81 m/s^2$ (meters per second second). So you should convert them to the same units before you divide, say write $l=0.5 m$.