Time period of a pendulum can be increased or decreased by changing th elength of the string of pendulum. The time period of the pendulum decreases as the length of the string increases and it increases as the length of the string decreases , hence time period is inversely proportional to the length of the string. The only things that affect the period of a simple pendulum are its length and the acceleration due to gravity. The period is completely independent of other factors, such as mass.
When analyzed, the pe- riod of the motion was found to be given by two multiplied by Pi multiplied by the square root of the quantity of the pendulum's length divided by the acceleration due to gravity. Therefore, the period , or time to complete a full oscillation, of a pendulum was found to be dependent on its length. One of the most common uses for pendulums is to tell time. The first pendulum clock was built in the s, and it was the most accurate way to tell time for nearly years.
Since the motion of a pendulum is a constant time interval, a pendulum inside a clock can keep the hands running on time. The longer the pendulum , whether it is a string, metal rod or wire, the slower the pendulum swings.
Conversely the shorter the pendulum the faster the swing rate. On grandfather clocks with long pendulums or clocks with shorter ones, the swing rate depends upon the pendulum's length. The Earth's gravity attracts the pendulum. This means that since the pendulum is now in motion, it keeps moving , unless there is a force that acts to make it stop.
Gravity works on the pendulum while it is moving. The moving force becomes less as the force of gravity acts on the pendulum.
The Period of a Pendulum. A simple pendulum consists of a light string tied at one end to a pivot point and attached to a mass at the other end. The period of a pendulum is the time it takes the pendulum to make one full back-and-forth swing. Oscillation is the repetitive variation, typically in time, of some measure about a central value often a point of equilibrium or between two or more different states.
Familiar examples of oscillation include a swinging pendulum and alternating current. The exact periods of your longer and shorter pendulums may be slightly less than 1. How Does Weight Affect Distance? The weight of an object influences the distance it can travel. Objects with a higher mass-density therefore travel faster and farther than those with a low mass-density, but only if they are launched with an infinite amount of force.
This will be accomplished by recording and analyzing data with the use of data tables and graphs. Research Question: How does string length affect the period time of the pendulum? Hypothesis: I believe that an increased string length with result in a longer period. Obtain a ring stand and attach a clamp, similar to figure 1.
Place the ring stand in an area that allows up to a cm length of string for the pendulum to move without any obstructions. Measure and cut cm of string and tie the string around the stopper. Secure the string on the clamp, similar to figure 1. Measure the length of the string from the ring stand to center of mass of the stopper.
It should be around 10cm. Record this length in the data table. Release the pendulum at this angle. Use a stopwatch to time 5 cycles and record the time in the data table. Repeat steps 5 and 6 two more times so there is a total of 3 trials for the same length of string. Record all data in the data table. Increase the length of string by about 15cm and measure the total length of the string.
Repeat this step along with steps nine more times. Table 1. The black pendulum is the small angle approximation, and the lighter gray pendulum initially hidden behind is the exact solution. For a large initial angle, the difference between the small angle approximation black and the exact solution light gray becomes apparent almost immediately.
Oscillation of a Simple Pendulum The Equation of Motion A simple pendulum consists of a ball point-mass m hanging from a massless string of length L and fixed at a pivot point P. When displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion. With the assumption of small angles, the frequency and period of the pendulum are independent of the initial angular displacement amplitude. A pendulum will have the same period regardless of its initial angle.
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