Lab 9 (2)

Name: Jivan Raghoo Date: 26/03/12 Title: Pendulum Aim: To investigate the oscillations of a chain of paper clips. Apparatus & Materials:    

Paper clips (25) Cork with hook attached to base Retort stand with boss Stopwatch

Diagram:

Figure 1 showing the set up of apparatus

Name: Jivan Raghoo Theory: Simple harmonic motion can be defined as the motion that occurs if the acceleration of a body is directly proportional to its distance from a fixed point and is always directed towards that point. The period of an oscillation, T, is the time taken for one complete oscillation. This experiment represents a simple pendulum undergoing simple harmonic motion. The equation for the period of a simple pendulum is: T =2 π

√

l g

This equation shows that T is directly proportional to l, the length of the pendulum. In this experiment l is dependent upon the number of paperclips, n. The equation given for T is: T = p nq Where, T is the period of oscillation n is the number of paper clips p and q are constants Method: 1. The cork was firmly clamped to the boss. 2. A chain of n paper clips was attached to the hook with an initial value of n=25. 3. The chain was displaced from its equilibrium position by moving the bottom clip sideways. 4. The time for 20 oscillations was measured and recorded. 5. The value of n was decreased in increments of 5 and the procedure was repeated until 6 readings were obtained. 6. All results were recorded in a table.

Name: Jivan Raghoo Variables: 1. Manipulated Variable: length of paper clip chain 2. Responding variable: period of oscillation Results: Table 1 showing values for the number of paper clips, time for 20 oscillations, period, log T and log n. No. of paper

Time for 20

Period (T)

log T

log n

clips (n) 25 20 15 12 10 7

oscillations1/ s 27.09 24.34 21.80 19.40 17.86 15.44

1.35 1.22 1.09 0.97 0.89 0.77

0.130 0.086 0.037 -0.013 -0.056 -0.114

1.40 1.30 1.18 1.08 1.00 0.85

Treatment of results: Gradient =

=

y 2− y 1 x 2−x 1 0.12−(−0.11) 1.38−0.86

= 0.44 From the equation, q

T=pn

We can take logs on both sides T =¿ lg pnq lg ¿

Name: Jivan Raghoo lgT =lgp+qlg n ∴lgT =qlgn+ lg p

y=mx +c Gradient = q Therefore q = 0.44 To find y-intercept we can sub in the values and a point on the line (1.38, 0.12) 0.12 = 0.44(1.38) + lg p lg p = -0.487 p = 0.33 δt=0.005 s

Precautions: 1. Displacement of paper clip must be less than 10o in order to ensure that motion is simple harmonic. 2. Windows were closed to reduce interference by environmental factors. Sources of error: 1. The timing did not always begin immediately as motion of oscillation becomes smooth and reproducible. 2. The oscillation of the paper clips were not always in one dimension, therefore the period was not exact. Conclusion: q = 0.44, p = 0.33