**P3 3.6**

Definition: a bob (a mass) swinging on a string.

For example, a playground swing, with the mass being the person on the seat.

How it works: The swing of a pendulum can be described by its:

**amplitude →**how far from the**vertical**(the dotted line on the diagram) the string moves.**time period**→ time taken for**one complete swing**.**frequency →**number of**complete**swings**per second**.

When a pendulum is swinging we say it is **oscillating**.

The **time period** is **directly proportional** to the **square root** of the **length** of the string:

The **frequency** of the oscillations is equal to **1** divided by the **time period**:

T = time period → unit: seconds (s)

f = frequency → unit: Hertz (Hz)

L = length → unit: metres (m) **examiners often trip students up by using cm or mm. Ensure you have converted all units before beginning your calculations.**

We can conclude by looking at the equations that:

the **longer** the pendulum → the **longer **the time period → the **smaller** the frequency

The time period of a pendulum can be affected by:

**mass**of the bob**length**of the string**amplitude**

#### Random Errors

Definition: an unpredictable variation around the true value, causing each reading to be slightly different.

So, basically, **mistakes**. These are often **human errors**. One very common, and unavoidable, human error is the **reaction time error**.

As you know, it takes us a moment to react, for example, there will be some **time** between **releasing the pendulum** to swing and **starting the stopwatch**.

This is on average **0.2 seconds** in humans.

To reduce the **impact** of this reaction time on results, record the time it takes for **several** oscillations to occur, such as **10 or 15**, and then find the **average**. This will make reaction time **almost ****negligible.**