Pendulum

IntroDUCTION

Pendulum is a weight suspended on a thread. Swinging back and forth, it oscillates about the equilibrium position (Figure 1). In ideal settings the thread should be inextensible (inelastic) and weightless. Since a thread that justifies such conditions does not exist, we use a thread whose weight is much smaller than the weight of a bob (Figure 2).

Definitions

OSCILLATION - full swing of a bob: right, left, and back to the position of equilibrium

AMPLITUDE - the size of the oscillations, or how far the pendulum swings back and forth

PERIOD T [s] - the time for one complete cycle.

FREQUENCY f [Hz or 1/s] - number of oscillations (or "events") per second.

Experimental Procedure

In this experiment, we will examine the relationship between the three characteristics of a pendulum, namely: the initial angle of the string, mass, and length. To examine these characteristics one at a time, we will perform three separate data collections (Part A, B, and C of this lab).

• Secure the thread in a way that will allow you to easy change its length (Figure 3).

• Measure the length (Figure 4).

• Weight the bob (Figure 5).

Part A. Investigating T(Ѳ)

In this part of the experiment, you will be changing the starting angle (Figure 6) of the swing. Both mass and length must not be changed in this part of the experiment (original length and mass) . What do you think will happen with the pendulum period? Will it decrease, increase, or remain the same as you change the angle of oscillation? Write down your prediction/hypothesis.

• Measure y (distance between the suspension and the ruler). Use tangent to find the angle

θ = tan^-1(x/y), x and y as shown in Figure 6.

• To increase precision, measure the time of 10 oscillations for the angle of 5° at least three times. Find the average time of 10 oscillations and divide by 10 to get the measured period.

• Repeat the steps above for a few angles.

• Collect your data in a table.

Derive a conclusion based on the collected data. Does the conclusion confirm your prediction?

Part B. Investigating T(m)

In this part of the experiment, you will be changing the mass of the bob. Both the angle of oscillation and length must not be changed in this part of the experiment (5° and the original length) How will changing mass affect the pendulum period? Write down your prediction.

• Add weight to the bob. Make sure that you do not change the pendulum's length.

• Measure time of 10 oscillations at least three times. Find the average time of 10 oscillations and divide by 10 to get the measured period.

• Repeat the steps above for at least five different masses.

• Collect your data in a table.

Derive a conclusion based on the collected data. Does the conclusion confirm your prediction?

Part C. Investigating T(L)

In this part of the experiment, you will be changing the length of the pendulum. Both the angle of oscillation and mass must not be changed in this part of the experiment (5° and the original mass) . What will happen with the pendulum period? Will it decrease, increase, or remain the same as you change the length? Write down your prediction.

• You can use measurement from part A as the reference point (5°angle, original length and mass).

• Measure time of 10 oscillations at least three times. Find the average time of 10 oscillations and divide by 10 to get the measured period.

• Double the original length. Repeat the steps above.

• Repeat the steps above for a few various lengths. The differences between various lengths should be more than 10 cm.

• Collect your data in a table.

Derive a conclusion based on the collected data. Does the conclusion confirm your prediction?

Part D. Comparing the experimental and calculated values

Calculate T using the provided formula

Find percent differences between the experimental and calculated value. What are the sources of error?

Explorations

1. Simple pendulum can be used to find the gravitational acceleration. Knowing the period of pendulum, find the gravitational acceleration g and compare to the accepted value of 9.81792 m/s² (source).

2. Since the value of g depends on the distance form the center of the Earth or altitude (Figure 7), is it possible to find the height of a hill or a skyscraper performing the described above experiment?