# Physics Pendulum Practical. How does the time period vary with length and what is the value of g?

Design

## Introduction

In this experiment, I am going to relate the time taken for 20 oscillations with the varying lengths of string used and use this relation to find the approximate value of ‘g’ or gravity.

I will do this by plotting the results of the experiment on a graph and using the gradient of the graph to find ‘g’. To do this, I will be using the formula below:

This can be rearranged to find the value of ‘g’:

## Research Question

How does the time period vary with length and what is the value of ‘g’?

## Hypothesis

I predict that the time taken for 20 oscillations will increase as the length of the string increases as they are directly proportional. As for the value of ‘g’, I predict that it will be approximately around 9.81 m/s2 as this is the standard value of ‘g’ that is accepted all around the world today.

## Variables

Controlled or Constant variables:

• Bob
• Mass of bob
• String used
• Amplitude of oscillation

Independent variables:

• Length of string

Dependent variables:

• Time taken for 20 oscillations
• Value of g (supposed to be constant variable)

## Manipulation of Variables

Controlled or Constant Variables:

• Bob: We used the same bob for all trials so that all the results acquired are relevant to one bob only.
• Mass of bob: Since we used the same bob for all trials, the mass of the bob did not change and remained constant for all trials.
• String used: We used the same string in all trials to maintain accuracy of the data.
• Amplitude of oscillation: We made sure that in each trial, the initial amplitude of the oscillation remained approximately 15°. This was hard to do but we tried our best in keeping it constant.

Independent variables:

• Length of string: For the string length, we took a wide range of 40-140cm (every 10 cm) and therefore we did trials with 11 different string lengths. We used a meter ruler to measure the length of the string for each trial.

Dependent variables:

• Time taken for 20 oscillations: We measured these using stopwatches and took 3 readings for each string length.
• Value of ‘g’: In reality, the value of ‘g’ is supposed to remain constant (approximately 9.81 m/s2). However, since our experiment is not perfect, the value of ‘g’ derived from our calculations might ...