OBJECTIVE: To measure the acceleration due to gravity using a simple pendulum.
Textbook reference: pp10-15
Many things in nature wiggle in a periodic fashion. That is, they vibrate. One such example is a simple pendulum. If we suspend a mass at the end of a piece of string, we have a simple pendulum. Here, the to and fro motion represents a periodic motion used in times past to control the motion of grandfather and cuckoo clocks. Such oscillatory motion is called simple harmonic motion. It was Galileo who first observed that the time a pendulum takes to swing back and forth through small distances depends only on the length of the pendulum The time of this to and fro motion, called the period, does not depend on the mass of the pendulum or on the size of the arc through which it swings. Another factor involved in the period of motion is, the acceleration due to gravity (g), which on the earth is 9.8 m/s2. It follows then that a long pendulum has a greater period than a shorter pendulum.
Before coming to lab, you should visit the following web site: http://www.myphysicslab.com/pendulum1.html This simulation shows a simple pendulum operating under gravity. For small oscillations the pendulum is linear, but it is non-linear for larger oscillations. You can change parameters in the simulation such as mass, gravity, and friction (damping). You can drag the pendulum with your mouse to change the starting position. I
With the assumption of small angles, the frequency and period of the pendulum are independent of the initial angular displacement amplitude. All simple pendulums should have the same period regardless of their initial angle (and regardless of their masses).
The period T for a simple pendulum does not depend on the mass or the initial angular displacement, but depends only on the length L of the string and the value of the gravitational field strength g, according to
The period T of a simple pendulum (measured in seconds) is given by the formula: T=2 π √ (L/g) T = time for 30 oscillations 30 oscillations (1) (2)
using equation (1) to solve for “g”, L is the length of the pendulum (measured in meters) and g is the acceleration due to gravity (measured in meters/sec2). Now with a bit of algebraic rearranging, we may solve Eq. (1) for the acceleration due to gravity g. (You should derive this result on your own). g = 4π²L/T2 (3)
1. Measure the length of the pendulum to the middle of the pendulum bob. Record the length of the pendulum in the table below. 2. With the help of a lab partner, set the pendulum in motion until it completes 30 to and fro oscillations, taking care to record this time. Then the period T for one oscillation is just the number recorded divided by 30 using (eq. 2). 3. You will make a total of eight measurements for g using two different masses at four different values for the length L.
Note: π = 3.14, 4 π² = 39.44
Time for 30 oscillations
Period T (seconds)
g = 39.44L/T2
Average value of g =
From your data what effect does changing the mass have on the period (for a given value of the length L)?
What role, if any, does air resistance have on your results? Explain your reasoning.
Would you conclude that Galileo was correct in his observation that the period of a simple pendulum depends only on the length of the pendulum?
On the moon, the acceleration due to gravity is one-sixth that of earth. That is
gmoon = gearth /6 = (9.8 m/s2)/6 = 1.63 m/s2.
What effect, if any, would this have on the period of a pendulum of length L? How would the period of this pendulum differ from an equivalent one on earth?
Purpose: To measure your personal reaction time. Discussion: Reaction time is the time interval between receiving a signal and acting on it – for example,...