Question

SIMPLE PENDULUM

1. What are the factors affecting the period of a simple pendulum?

1.1. What must you do to the length of a simple pendulum so that its period is doubled?

1.2. Determine the acceleration due to gravity in a location where a simple pendulum is 150.0 cm long makes 100 vibrations in 246 s.

1.3 What can you conclude from the graph? (Chegg on my laptop wouldn't let me upload so I've attached the link) - http://tinypic.com/r/j6o5qq/9​

Answer 1

The time period of the simple pendulum of length L and in gravitational field g is
   
1)
  So, the time period depends upon the length L of the pendulum and the gravitational field g.
1.1)
As T is proportional to the square root of L, so, we need to increase the length four times ( L' = 4L) in order to increase the period twice (T' = 2T).
  


1.2)
  The time period in this case is
     
And the length of the simple pendulum is
   
So, the acceleration due to gravity is


So, putting the given values, we get
  


1.3)

   If take the square of the time period, then we get
  
So, the plot of   is a straight line passing through the origin and is of the form with a slope given by
  
So, from a given curve we can calculate the slope and if the slope is known, then we can calculate the acceleration due to gravity
   

And from the given graph, the slope is approximately
   
So,
  

However this value is smaller than the exact value (9.8 m/s^2).