Simple Pendulum

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QUESTION

The apparatus for this experiment consists of a string of about 20cm or 30 cm long, a bob, a ruler, a stopwatch.

Alternatives: a thin ribbon of width 0.4 or 0.5 cm cut from bounty paper of 20 cm long, two candies (cough drop candy), tape, ruler, cell phone stopwatch.

Experimental Setup
Take a bounty towel and cut a thin ribbon sized paper from the width of the bounty towel and then stick a candy at the end of the ribbon on lower end with a tape. This is your hand made, homemade simple pendulum.

Now hold it one your one hand in between thumb and fore finger and measure its length from the point you hanging to the center of the candy. It is length of the pendulum, L.

Time period of a pendulum
Set up the pendulum with maximum length L1 = 20 cm or 30 cm what you have; Length of the pendulum is measured to the center of the bob.

Now use your phone as a stopwatch and get ready to measure time of oscillation in seconds. Now give a deflection to your pendulum by moving bob or candy on one side on the pendulum. Don’t release it until you are ready to start stopwatch. Now release it counting as zero and also start your stopwatch at the same time. Keep counting oscillations when candy comes back to the same spot where it started for next number of oscillations. You may do a test to see how your pendulum oscillates and how long it oscillates. Now measure time of oscillation for at least 5 or 8 or 10 oscillations based on how long your pendulum oscillates. This is your experimental time of oscillation for n oscillations. Now find out experimental time period by taking total time t1/n for one oscillation and it is Texp1 = t1/n.
Now calculate time period theoretically Tth1 of oscillation using equation for a given L. Make sure to use value of L in m and g in m/s^2 using formula given below:
Tth=2π√(L/g)            …1
Record your values of L1, t1, n, Tth1, Texp1 for this experiment. Compare your Tth1 and Texp1.
L1 = _________ cm = __________ m; t1 = __________ s,  n = _________;
Texp1 = t1/n = ________ s; Tth1 = ________ s
Calculate the percent error between the experimental and theoretical values of t.
% error = [(Tth1 – Texp1)/Tth1]*100 =
Effect of length on time period

Now make change length of the string or ribbon shorter, half of the first one, L2 = 10 cm and repeat the experiment with same bob or candy and same amplitude or deflection as you did before for same number of oscillations and record t2. Then find Texp2 = t2/n. Now find your new theoretical time of oscillation using the same formula but now length will be half and make sure to use new L in m again to get Tth2. Record values and write as given below.
L2 = _________ cm = __________ m; t2 = __________ s,  n = _________;
Texp2 = t2/n = ________ s; Tth2 = ________ s

Tth2 =

Texp2 =

% error =
       (c) Effect of Mass on time period
The formula for the period T does not contain the mass of the bob and hence the period should be independent of the mass of the bob. To verify this, repeat the experiment with two bobs or two candies. To do that add another candy on the same set of pendulum on other side of the ribbon with tape. Make sure both cadies are at the same height or distance from the top of the pendulum.
Now, repeat your experiment with two bobs (heavier mass) for same original length L1 = 20 cm keeping length same, Amplitude same and find out your new t for the same number of oscillations. Now calculate new time period Texp3 (show your work) = t3/n. Record your values as shown below:
L1 = _________ cm = __________ m; t3 = __________ s,  n = _________;
Texp3 = t3/n = ________ s; Tth1 = ________ s

Picture 1: showing movement of pendulum with its SHM movement.

Now, calculate percent difference between Texp1 and Texp3 (show your work).
%error = [(T1exp  –  T3exp)/ (T1exp  +  T3exp)/2]*100 =

Answer following questions:
1.If length of the pendulum increases, what will happen to its time period?

2.If amplitude of oscillation increases, what will happen to its time period?

3.If mass of the bob increases, what will happen to its time period?

4.Do you think your experiment satisfies the equation 1 of simple pendulum?

5.Are your results consistent in every part of the experiment? If not, what could be the reasons and how it can be fixed?

6.Can you give an example from the real world where you can see the concept of simple pendulum?

7.What will happen to the period of pendulum if you take it to the moon where g = 1.6 m/s2?

Sample Solutions
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