# Homework Help: Mplitude of a pendulum from an angle vs time graph

1. Nov 20, 2009

### MisterM

1. The problem statement, all variables and given/known data
A student studies a long pendulum by measuring the angle that the string makes with the vertical as a function of time t. What is the angular frequency of the pendulum? What is the amplitude of the motion?

I'm given an angle vs time graph which is sinusoidal. The amplitude on the theta (degrees) vs time (seconds) graph is 2 degrees, and period is 1.5 seconds. My angular frequency is 4.19 rad/s. This is all that I know, and I need to find the amplitude of the position vs time graph.

As far as attempts and equations are concerned, that's my problem. I don't know how I can find the answer. I've been looking at Vmax equations of a pendulum but they all have A in them, and I know that since the angle is small I'm allowed to approximate sin theta = theta in radians, but I still have no idea where to go from here.

Edit: I was able to find the answer using the equation: A = Θmax*L, substituting L = g/ω² and reading Θmax as being the amplitude on my Θ vs time graph (converted to radians).

A = Θmax*g/ω² = [(2°)*(π rad/180°)]*[(9.8 m/s²)/(4.19 rad/s)²] = (0.03491)*(0.558) = 0.0198

Sorry for having my post be all disorganized.

Last edited: Nov 21, 2009
2. Nov 20, 2009

### ideasrule

If the pendulum's period is 1.5 s, how long is the string holding the pendulum? If you know the length, can you figure out the max. height (and max. x coordinate) the pendulum reaches?

3. Nov 21, 2009

### Redbelly98

Staff Emeritus
What is the actual question? It seemed to be "What is the angular frequency of the pendulum?", which you later answered as 4.19 rad/s. If you are also asked to find the amplitude, can't you just get that off of the graph?