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| Simple Pendulum – Time Period of Oscillation Varies with Time |
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| Let us now find out how Time Period of oscillation vary with time. |
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| Set up a simple pendulum and measure the time taken for 10 oscillations of the simple pendulum for different lengths like 10,20,40,60,80 and 100 cm. |
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| Time period of a pendulum varies with the length of the pendulum |
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| The above table shows that time period of a pendulum varies with the length of the pendulum. But the above table does not tell us whether the length and time period are directly proportional or not. By plotting a graph between L and T we can come to know whether L and T are directly proportional or not. |
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| We plot a graph by taking L along x axis and T along y axis, |
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| Graph between length and time period of a pendulum |
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| The T vs L graph is not a straight line but it is a parabola. From this we can infer that length of the pendulum is not directly proportional to the time period. The T vs L graph is a parabola and it suggests that the square of the time period is directly proportional to length of the pendulum. Now if we plot
T2 against L, the graph will be a straight line. |
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| The table below gives the value of L and T2 |
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| Graph between length and square of the time period of a pendulum |
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| L and T2 plot is a straight line indicating that length is directly proportional to T2, |
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Experimentally the value of the constant of Earth is found to be equal to
0.248m/S2 and mathematically 0.248 if found to be equal to 
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| value of g (acceleration due to gravity) |
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| From the above relation we can derive a formula for time period |
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| The equation (1) suggests, |
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i.e., time period is directly
proportional to the square root of the length of the pendulum and  i.e., the time period of the
pendulum is inversely proportional to the square root of the acceleration due to gravity. |
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| From the equation (1), we conclude that time period of a pendulum does not depend on the mass of the bob. |
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| A harmonic oscillation of constant amplitude is called simple harmonic motion (SHM). The simple pendulum executes simple harmonic motion about the mean position. |
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| A simple pendulum whose time period is two seconds (i.e., on Earth) is called a Seconds Pendulum. A Seconds Pendulum is used in Pendulum clocks. |
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