Objective:

To determine the oscillation or length of a pendulum.

General:

• For small angles of θ° from the perpendicular,

the period of the simple pendulum can be found by the formula:

where l is the length of the pendulum and g is the acceleration due to gravity.

• A relationship to determine the length of the pendulum or the oscillations per minute can be set on the slide rule by using the B, C and D scales.  However some simplification of the formula must be done first.  T is the period in seconds, in other words how long each oscillation takes (one to and fro movement).  The inverse of T, the frequency is how many oscillations per second.

• Squaring the expression of gather the constants:

 

• The value in front of 1/l on the right hand side is a constant (depends slightly where you are on the earth).  Evaluating this constant ...

• So we have the following expression that will give the number of oscillations per second.

• For the number of oscillations per minute, we multiply by 60:

• Giving the following expression for the number of oscillations per minute:

Method to find the Oscillation of a Pendulum:

• Move the cursor to D187.5.
• Align the pendulum length on B with the cursor.
• Read the oscillations per minute on the D scale at the C index.

 

Method to find the Length of a Pendulum:

• Move the cursor to D187.5.
• Set the index of C at the pendulum length on D.
• Read the result length of the pendulum in inches at the cursor on the B scale.

 

Example 1:  How many oscillations per minute will a 48" long pendulum make?

• Move the cursor to D187.5.
• Align B48 with the cursor. (second decade)
• Read the result at D27. (at C index)
• Answer: 27 oscillations per minute.

Example 2:  What is the length of a pendulum making 40 oscillations per minute?

• Move the cursor to D187.4.
• Set C10 at D40.
• Read the result at the cursor, B22.
• Answer: 22"

Practice Questions:

1. How many oscillations per minute will a 56" long pendulum make? (Ans: 25)
2. What is the length of a pendulum making 60 oscillations per minute? (Ans: 9.8")