Question

Summarize this experiment of pendulum from purpose to procedure to analysis.
Within your answer, include the theoretical equations.

Answer 1

the purpose of the experiment is to measure the gravitational acceleration of the earth using pendulum.

Procedure

To simplify and systematize the data-taking and analysis, confine our experimental values for pendulum length to the values

15, 20,25,20 cm

Use values of amplitude angle of

5, 30 and 70 degrees,

measured from the vertical.

(1) Attach a string to a rigid support high above the floor.The attachment point must be solid so that it does not shift position as the pendulum swings.

(2) ln all cases set the pendulum into motion so it swings in a fixed vertical plane. Avoid oval paths, because they introduce other variables which are hard to control.

(3) Choose the largest practical value of string length (from the list above). Keeping this length constant, investigate the effect of bob mass on the period by successively testing each of the different bob samples provided. Use an initial amplitude of 5 degrees in all cases.

(4) Using the same string length, and the heaviest metal bob, investigate the effect of different amplitudes. Use the amplitude angle values from the list above.

(5) Use a metal bob and an initial amplitude of 5 degrees. Then try successively shorter string lengths. Use the length values from the list above. For the shorter lengths we will have to time more swings to keep the accuracy of the pendulum period comparable to that for the longer lengths.

(6) compare the periods of a plane pendulum and a spherical pendulum with the same string length and the same bob. A spherical pendulum is one in which the bob swings in a perfect circle in a horizontal plane.

ANALYSIS

The data will very likely show that the strongest dependence is that of the period on the string length. Plot the data for the metal bob: period versus length, on ordinary (linear) graph paper. The plotted points will lie on a curve. The direction of its curvature leads one to suspect that an equation of the form

.

T = K L^{n ------1}

Take the logartithm of both sides:

.

log(T) = log(K) + n log(L) ----2

Consider two well-separated points on the straight line, P1 and P2. Write Eq. 2 twice, once for each point.

[3]

log(T₁) = log(K) + n log(L₁)

[4]

log(T₂) = log(K) + n log(L₂)

Subtract Eq. 4 from Eq. 3.

log(T₂) - log(T₁) = n[log(L₂) - log(L₁)]

So, finally,

[5]

log(T₂) - log(T₁) n = ————————————————— log(L₂) - log(L₁)

Use this to determine the value of n.

Also determine, from the graph, the value of K. estimate the error in each of these results.

(4) Finally, examine the data to see whether the period depends on any other variables to a degree significantly larger than the experimental errors. State clearly what can be concluded about such dependences, from the data.

(5) An theoritical data asserts that the period of a simple pendulum is given by the equation:

[6]

T = 2π√(L/g)

where g is the acceleration due to gravity (about 9.8 m/sec). Compare this with actual data.

(6) Using our value of the slope K from analysis section (3) and equation [6] determine the acceleration due to gravity, g.