Simple harmonic motion of a simple pendulum Essay Example

Simple harmonic motion of a simple pendulum Paper To work out the value of acceleration due to gravity (g), by using the principle of kinematics of simple harmonic motion of a simple pendulum.  Introduction-  The theory involved here is the motion of the simple pendulum under the influence of acceleration due to gravity. The research question here says that the value of acceleration due to gravity is an unknown variable and this has to be calculated out using the equation that relates the time period of one oscillation of a simple pendulum (made up of a string with negligible mass and a mass bob having a certain predetermined and set mass) and the length of its string and acceleration due to gravity by the following relation: This investigation is particularly useful in the real world as it gives us a value of the variable acceleration due to gravity, which influences all spheres of mechanics. The equation is also useful as I help determine the value of time that the pendulum will take in one oscillation, thus having applications in instruments such as clocks etc.  Hypothesis-  According to my prior understanding and visualizations the investigations undertaken will yield the required results effectively and with efficiency. The length of the pendulum would include the length of the string as well as the diameter of the mass bob and the length of the hook as well. When the pendulum suspended from a stand is set into oscillation the time periods T of the oscillations of different lengths l will help us in determining the value of g. As the length of the string is increased, the time period of the oscillations will also increase but the value of g will not as it is constant for a place always. The accepted value for g (in Paris) is 981Nkg-1 according to .We should get a value of g of the range of the value above stated. The master equation also as stated earlier will be modified in order to calculate out the value of g. We will write a custom essay sample on Simple harmonic motion of a simple pendulum specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Simple harmonic motion of a simple pendulum specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Simple harmonic motion of a simple pendulum specifically for you FOR ONLY $16.38 $13.9/page Hire Writer The basic theory behind the experiment is that the value of the time period taken by the pendulum in one oscillation is influenced by the length of the string which is supporting the pendulum and the value of acceleration due to gravity. By modifying the equation stated above as follows, the value of g can be found out using a simple equation. The variables in the experiment are g which is acceleration due to gravity which is our measured variable; T is time period which is the dependent variable which we be observing; l is length of the entire pendulum out of which we will be controlling only the length of the string as the length of the hook and the mass bob will be the same; finally ? is the constant variable. 1. Tie the string to the mass bob of unknown weight and suspend it from the table stand as shown in the diagram. Make sure that the two small blocks of wood are in such a position that they clamp the pendulum and they are in turn clamped by the clamp of the stand.  2. In order to get proper value that will be finally calculated out I have decided to take 5 readings of the oscillations of the pendulum using four different lengths of the pendulum (20cm to 90cm) so as to remove most possibilities of random errors. 3. To begin with the length of the string of the first reading is determined so that the length of the mass bob may also be incorporated in it so as to get a convenient length of the pendulum.  4. When the apparatus is set up as shown in the diagram described earlier, the pendulum is taken and set to a particular angle not more than 15 degrees from its mean position.  5. the pendulum is then left and it sets into motion. The time period for 10 oscillations is seen and recorded with a stopwatch. 6. To obtain the mean value of one oscillation of the pendulum of length 30cm, the total time taken for all oscillations is divided by 10 which is the number of oscillations which the pendulum is allowed to swing for.  7. This procedure must be repeated four more times and then after the data has been collected for all five times, the average value of these will be taken as the final reading of the time period of the simple pendulum of length 20cm.  8. Repeat the entire process of experimentation with all the different lengths of the pendulums and tabulate the data.  9. After tabulation of data, it must be processed to obtain the appropriate results. The data collection and processing aspect is seen later in this report. Collection of Data   On taking readings with vernier calipers, the diameter of the mass bob was found out to be 2.55cm. The vernier calipers showed a positive zero error of 0.09cm. Thus the diameter was found out to be 2.55 0.09 = 2.46cm. The radius of the mass bob is thus 1.23cm. The length of the hook again measured with vernier calipers was found to be 1.25cm, which after adding for the zero error will be 1.25 0.09 = 1.16cm. Thus the length of the entire system of the mass bob and the hook is 2.39cm.