- Make sure that the pendulum swing in a vertical plane.
Explanation：If the mass does not oscillate vertically, some of the kinetic energy will be wasted. And its displacement of oscillation can not be described by harmonic functions. Thus, the oscillation is not a simple harmonic motion.
- Count the oscillation when the bob reaches the most right-hand side or most left-hand side.
Explanation：As when the bob swung forward to the most right-hand side and swung back to the left-hand side, it can be said as a completed oscillation.
- Timing should be aborted if the oscillation of the pendulum bob becomes elliptical.
Explanation：As the bob must be swung in a vertical plane in order to obtain an accurate reading of corresponding period, if the oscillation of the pendulum bob becomes elliptical, the oscillation is not simple harmonic motion any more. Thus, the taking of the time becomes meaningless and the timing should be aborted and starts a new one.
Table of data
Theory
When the string makes an angle θ with the vertical, the displacement of the
bob is the arc length given by x = (H-d)θ……(1) and the restoring force acting on it is along the tangent, given by F = –mgsinθ……(2). See Fig c, the net force causes the bob to accelerate towards the equilibrium position, given by F = ma = –mgsinθ……(3). For small angleθ, we have sinθ〜 ……(5). Putting (5) into (3), we have ma〜–X, or a = –X……(6) for small amplitude. Hence the motion is simple harmonic and the period is T = 2π√. By taking square on the both side, T² = (H-d)……T² = –d + H,
Where –is the slope and H is the y-intercept.
Calculation
The slope m = = –4.07
∵Slope = – ∴Acceleration due to gravity (g) = = 9.69
The maximum slope m+ = = –4.21
The maximum slope m- = = –3.13
∣m+－m∣= 0.137
∣m -－m∣= 0.940
∴The maximum error in slope △m = 0.940
Percentage error in slope =∣ × 100%∣
=∣ × 100%∣
= 23.1%
The maximum error in g = 9.69 × 23.1% = 2.24
∴The acceleration due to gravity g = 9.69 ± 2.24
An interpretation of the results
The value of g reflects the reality of the errors appeared in the experiment. We can see that the maximum possible error is really large, thus, it affects the expression of the answer which is inaccurate. On the other hand, I gain some experiences from obtaining the value of the maximum possible error, that is we need to be absolutely concentrated to each set of the data we take, and pay attention to every timing as any one of the timing which is carelessly taken will influence the slope of the line at the graph. Finally, it causes the serious inaccuracy
Discussion
- Discuss the difficulties and limitation of the experiment
Ans：It is difficult to take the time of oscillation accurately / It is impossible for the man to use hand so as to let the pendulum swing in a vertical plane / the string used must be at least one meter long
- The sources of errors in the experiment
Ans：The pendulum does not oscillate exactly in vertical plane / The reaction time of the observer when he starts timing for beginning and the stopping of the oscillation will cause the human error and lead to the inaccurate reading of time / there exists friction where the string is nailed to the coins and affects the mechanical energy of the pendulum bob system.
- Suggest improvement to the experiment
Ans：Using motion sensor rather than timer to record the oscillation of pendulum bob which is the simple harmonic motion
- Discuss how the value of H can be determined
Ans：By the equation T² = (H-d), we know the value of T²,and d, so we can solve the value of H.
Conclusion
From the experiment, we obtain that the acceleration due to gravity (g) is 9.69 ± 2.24, the period of the oscillations of the pendulum varies inversely as the distance of the pendulum bob from the ground. It is very difficult to carry out the mechanical experiment accurately as many errors must be existed.
