Does the length of the string or weight affect the swing speed of a pendulum ?

Problem/Question

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To see how the length of the string L affects the swing speed of the object attached (simple pendulum); Also, to check if the weight of the object m will affect the swing speed if the length of the string is constant.

Hypothesis/Conjecture

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• The longer the length of the string, the slower it swings, and the shorter the length of the string, the faster it swings.
• The heavier the object attached, the slower it swings, and the lighter the object attached, the faster it swings.

Materials

• String
• Objects with different weight
• Timer
• Tape measure
• Pair of scissors
• Scale to measure the weight
• Tripod to hang the pendulum
• Pen and paper to record the results

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Procedure

Hypothesis I

• Cut the string
• Attach to a weight (I use a screw socket)
• Hang the string and weight to a tripod
• Measure the length of the string from top to the half height of the weight
• Pull the weight away and release, at the same time, start the timer
• Let it swing 10 complete cycles
• Stop the timer and record the time
• Write down the results
• Repeat two more times from step 5 to step 8 for the same length
• Change six different lengths of strings and repeat step 4 to step 9

Hypothesis II

• Keep a same length of string
• Measure a weight
• Attach the weight to the string
• Pull the weight away and release, at the same time, start the timer
• Let it swing 10 complete cycles
• Stop the timer and record the time
• Write down the results
• Repeat two more times from step 4 to step 7 with a same weight
• Change six different weights and repeat step 2 to step 8

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Data Tables

Table 1. Time needed to swing 10 complete cycles for 6 different string lengths

with weight = 101 (g)

Table 2. Time needed to swing 10 complete cycles for 6 different weights

with string length = 52.3 (cm)

Period vs. Length and Weight

The period T of a simple pendulum is defined as the time needed to swing one complete cycle. So the measured average time needs to be divided by 10 to get the time for one complete cycle (period). The length of string was also converted to meter (m) and weight was converted to kilogram (kg) for standard metric system.

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Table 3. Swing Period for 6 different string lengths. ( Weight m = 0.101 kg )

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Table 4. Swing Period for 6 different weights. ( Length L = 0.523 m )

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Period of pendulum

Materials

During the experiment

Conclusion and Proofs

The first hypothesis was supported: The longer the string, the slower it swings so the larger the period; and the shorter the string, the faster it swings so the smaller period.

The second hypothesis was not supported. The hypothesis was: the heavier the weight, the slower it swings, but the test shows it doesn’t change that much and it doesn’t matter whether the weight is heavy or light. The period of a simple pendulum is just depended on the length of the string.

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Real World Connections

• Keeping the time

Since the motion of a pendulum is a constant time interval, a pendulum can be built inside a clock that can keep the hands running on time. Since the 1600s, the pendulum has been used in clock for 300 years, even nowadays, we still see the clock with the pendulum.

• Metronomes

A pendulum can be built into a device that emits a click or a light for each beat of a predetermined interval for helping people to play music notes.

• Amusement park and playgrounds

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