### Pendulum Motion

To determine the relationship between the period of a pendulum and various factors, assessed individually, which are the mass of the pendulum, length of the attached string, and angle of release. THEORY AND HYPOTHESIS: Many factors affect the swinging motion of a pendulum. My design lab intends to reach a conclusion on the factors that do, and do not, affect the motion of a pendulum. I hypothesize that the mass of the pendulum will not affect the period because the acceleration of gravity is the same for all masses on Earth. The length of the string will affect the period because it affects the distance that the pendulum travels. The angle of release should also affect the period because it also changes the distance the pendulum travels in a period.1.

Gather all materials.2. Tidy and clean lab table.

Part 2- Mass 1. Attach ring clamp to ring stand. 2. Cut a piece of string noticeably longer than 30cm. 3. Tie the 15g weight to the string.

4. Adjust the string such that the weight is 30cm from the ring. 5. Secure string to the ring clamp with tape and hand. 6. Make sure the pendulum is horizontal (180 degrees to the horizon) 7. Release and record time of one period (when the pendulum swings away and back once).

8. Perform five trials and calculate the average period . 9. Repeat with other weights.Length of String 1.

Repeat steps 1 to 6 from the part 1 using a 100g mass and 10cm string. 2. Release the weight and record time of one period. 3. Repeat with the same weight using 20cm, 30cm, 40cm, and 50cm strings. 4. Perform five trials and calculate the average period.

Part 3 – Angle of release 1. Repeat steps 1 to 6 from part 1 using a 100g mass. 2. Adjust the angle of release such that it is 180 degrees from the horizontal. 3. Release and record time of one period. 4.

Repeat with the same angle using 195, 210, 225, 250 degrees from the horizontal.5. Perform five trials and calculate the average period. Looking at Graph 4, we can observe a direct and proportional relationship between the angles of release and the average period, similar to that of Graph 3. As I hypothesized, the angle of release directly affects the average period because as the angle comes closer to the vertical the object has less distance to travel in a period. And when the distance an object travels is decreased without changing the acceleration, period is decreased.

Similar to the explanation to Graph 3, when the distance is decreased (angle approaching 270) and acceleration remains constant, the time it takes for one period is also decreased. Therefore, the angle of release and the average period of a pendulum motion are directly related.CONCLUSIONS:There is a proportional relationship between length of string and the period as represented by the equation l= 49cm/s (T) + 6cm, where l is the length, T is the period, and a line is produced. There is a proportional relationship between the angle of release and the period as represented by the equation a= 233s (T) + 255, where a is the acceleration, T is the period, and a line is produced.

Theoretically, there is no relationship between the mass and the period; however, since there is air resistance in the laboratory, large objects have bigger drag and take longer to complete one period. The equation T= V (2.54×10-4 s/g (m) + 0s) represents the length of the period as a function of the mass; as we can see from the equation, the mass will not have a significant impact on the period of the pendulum motion. There is no accepted value for this design lab; therefore, it is inappropriate to designate an arbitrary value to compare to my measured value.