# Determine pendulum's maximum angular displacement

[SOLVED] Simple Pendulum

## Homework Statement

A simple pendulum with a length of 1.23 m and a mass of 6.64 kg is given an initial speed of 1.96 m/s at its equilibrium position.
(a) Assuming it undergoes simple harmonic motion, determine its period.
(b) Determine its total energy.
(c) Determine its maximum angular displacement. (For large v, and/or small l, the small angle approximation may not be good enough here.)

## The Attempt at a Solution

I have solved up to part c), and I can't figure out how to set it up. I thought at first it was
.5mv^2 = mgh and then solving for h, but once I get h I am not sure what to do. Can someone help me get this set up? Thanks.

## Answers and Replies

dynamicsolo
Homework Helper
I thought at first it was
.5mv^2 = mgh and then solving for h, but once I get h I am not sure what to do. Can someone help me get this set up? Thanks.

That is what you want to do. So the pendulum bob is now at a height h (what is the value?) above the bottom of the pendulum's arc. Draw a picture of the pendulum tilted off the vertical so that the length of the pendulum is 1.23 m and the bob is at a height h from the lowest point of the swing. The pendulum shaft is now the hypotenuse of a right triangle. What must the altitude of that triangle be? From that, how do you find the apex angle of that triangle?

Excellent, made sense. Thanks for the help