Pendulum Practical - Physics

• Experiment to find gravitational acceleration using a pendulum


  1. Arrange a simple pendulum

  2. Give a small horizontal displacement

  3. Measure time for full oscillations

  4. Repeat with different pendulum lengths

  5. Plot graph of t^2 vs L

  6. Calculate gravitational acceleration from graph
• Gravitational acceleration


  Denoted as G, typical value is 9.8 or 10 m/s^2
• Simple pendulum


  • String and small ball
  • Oscillates through small angle (5-7 degrees)
• Changing pendulum length L

  Changes time period T proportional to √L
• Measuring time period


  1. Measure time for 20-25 oscillations

  2. Reduces fractional error in timing
• Pendulum bob


  • Should be made of dense material like metal
  • To minimize effect of air resistance
• Suspending the pendulum


  • Use a cork with vertical slit to avoid changes in effective length
  • Measure length from suspension point to center of bob
• Using a locating pin


  1. Place pin vertically below pendulum path

  2. To precisely count number of oscillations
• Larger changes in pendulum length L are better to see significant changes in time period T
• Fixing the pendulum


  1. Measure the length from the point where the thread starts to the center of gravity of the pendulum ball

  2. Ensure the thread is vertical and fix the locating pin perpendicular to the thread
• The equation for the period of oscillation is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity
• Measuring the period of oscillation

  1. Give a small angular displacement to the pendulum

  2. Measure the time for 20 oscillations

  3. Divide the total time by 20 to get the period of one oscillation
• As the length of the pendulum decreases


  The period of oscillation decreases
• The theoretical period calculated using the equation matches the experimental values obtained
• Measuring the period for 20 oscillations reduces the percentage error compared to measuring for a single oscillation
• Measuring time for 20 oscillations

  1. Reset stopwatch to zero

  2. Give small oscillation

  3. Start stopwatch

  4. Count 20 oscillations

  5. Stop stopwatch
• Time taken for 20 oscillations is 40 seconds
• Calculating time period using equation

  1. T = 2π√(L/g)

  2. Cancel π and √g

  3. T = 2√L

  4. L = 1 meter

  5. T = 2 seconds
• Time period calculated is 2 seconds, which matches the measured 40 seconds for 20 oscillations
• Measuring time for 20 oscillations at different lengths

  1. Reduce length by 25 cm to 75 cm

  2. Observe 20 oscillations

  3. Time taken is 35 seconds
• Time taken for 20 oscillations at 75 cm length is 35 seconds
• Experimental setup


  • Pendulum ball and indicator must be at eye level for precise observation
  • Experimenter should sit in front of the pendulum
• Measuring time for 20 oscillations at 75 cm length

  1. Give small displacement

  2. Start stopwatch

  3. Count 20 oscillations

  4. Stop stopwatch
• Measurements recorded for 5 different lengths and corresponding times for 20 oscillations
• Analyzing the data


  1. Plot t^2 vs L graph

  2. Verify if it is a straight line through origin

  3. Calculate gradient to find g
• Gradient of the t^2 vs L graph is 4π^2/g
• Calculated value of g is 10 m/s^2, close to the theoretical value of 9.8 m/s^2
• Slight deviations in the experimental values are due to measurement errors like air drag, timing errors etc.
• Simple pendulum


  Pendulum with a uniform metal sphere as the bob
• Analyzing the t^2 vs L graph

  1. Gradient = 4π^2/g

  2. Intercept = 4π^2r/g

  3. Solve for r
• Radius of the metal sphere bob is 1 cm
• Wooden sphere vs metal sphere as pendulum bob

  Wooden sphere will damp faster and come to rest faster due to higher air drag impact
• Foreign is more than that of more than that on which one the other one wooden sphere of the same radius the student observe the amplitude of oscillations gradually decreases with time and the Bob finally comes to rest due to the track he repeated the above experiment with the wooden radius so what was the previous one he used uniform metal sphere
• metal sphere clear simple simple to understand see from Top If you put a metallic ball and a Woolen ball wool the metallic ball Falls faster same size Woolen ball because of the art drag sometimes it might not even fall directly it might you know go here and there and fall it takes more time which means the impact of Air drag depends on the weight not only the size even though the size is same the metallic ball will fall faster than the Woolen ball
• similar concept is therefore pendulum also metallic ball and the wooden ball wooden ball is less weighted therefore it will have more impact due to the attract clear right
• Figure 1 shows the motion of a simple pendulum of length l write down an expression for the period of oscillation te of the simple Pendulum

  T equals 2 pi square root of L over G
• if the laboratory experiment to find the value of G using the simple pendulum you are provided with a stopwatch which which can measure the time with an accuracy of 0.5 seconds if the estimated value of the period T is two seconds determine the maximum number of oscillations you should take to reduce the percentage error of T down to one percentage
• a student has designed an electrical method to determine the period of oscillation T more accurately by using a detector system
• Source diode


  Emits a narrow beam of infrared light with a constant intensity of L naught
• Detector diode


  Detects the intensity of the infrared beam