# Hanging pendulum, what is mean by period of small amplitude oscillations of the bob?

1. Oct 1, 2014

### Tangeton

A simple pendulum is suspended from a ceiling 3.2m high and the bob height from the floor is measured to be 68cm. Calculate the period of small amplitude oscillations of the bob.

I converted 68cm to 0.68m. The total length of the pendulum must be 3.2 - 0.68 = 2.52. When working with the period, T = 2 pie x sqrt of l/g, do I use my l as 2.52 or half of it since I'm working out the period of the amplitude? And what does it mean by small amplitude... is it just small because it doesn't fallow for big values of amplitude?

2. Oct 1, 2014

### Staff: Mentor

For small amplitude swings, the period is practically independent of the amplitude of the swing. For larger swings, the amplitude appears in the formula for the period, meaning it's no longer SHM. oo)

3. Oct 1, 2014

### BvU

Could you explain what made you write this ?

4. Oct 1, 2014

### Tangeton

Amplitude is at its peak at T/2, half way through an oscillation...

5. Oct 1, 2014

### Tangeton

Please someone just confirm its length is 2.52... no matter how much my lack of understanding is making you suffer right now...

6. Oct 1, 2014

### Staff: Mentor

In metres, yes.

You will find this topic well-treated in many online resources. Use a google search.

7. Oct 1, 2014

### BvU

Look up Amplitude (that is a hyperlink, but on my screen it is indistinguishable from normal text; http://en.wikipedia.org/wiki/Amplitude. Use number 1 as the normal definition) and realize that
is not right. Amplitude is a constant for undamped harmonic oscillation.
If the deviation from equilibrium is $x = A \sin(\omega t)$ then x = 0 at T/2 !

The exercise mentions oscillations with small amplitude because then the restoring force ($-mg \sin\theta$) can be approximated by $-mg\theta$ and that leads to simple harmonic oscillations.