Model No:SPH-M009
To estimate the time period of a simple pendulum using the theory of errors, graph-Gaussian distribution
The time period (T) of a simple pendulum is estimated by measuring multiple oscillations, calculating the mean and deviations from repeated trials, and analyzing the random error distribution using a Gaussian (normal) curve
The time period (T) of a simple pendulum is estimated by measuring multiple oscillations, calculating the mean and deviations from repeated trials, and analyzing the random error distribution using a Gaussian (normal) curve.
Time Period Formula: T = 2π √(L / g)
Where L is the effective length of the pendulum and g is the acceleration due to gravity.
Linearized Relation (L - T² Graph): T² = (4π² / g) * L
Plotting T² on the y-axis against L on the x-axis yields a straight line whose slope helps determine g or verify period consistency.
1. Set up the Pendulum: Suspend a small heavy bob with a fine, inelastic thread from a rigid stand to define the effective length L = l + h + r (thread length + hook + bob radius).
2. Collect Data: Measure the time (t) for n = 20 oscillations using a high-precision stopwatch (resolution ≥ 0.1 s or 0.01 s). Repeat the measurement N times.
3. Calculate Periods: Find the time period for a single oscillation as T_i = t_i / n for each trial.
4. Compute Mean & Errors: Find the arithmetic mean T_avg. Calculate individual deviations x_i = T_i - T_avg and their squares x_i². Determine σ and probable error R.
5. Plot the Gaussian Distribution: Create a frequency distribution table of the deviations (x_i) rounded to decimal places. Plot frequency on the y-axis versus deviation on the x-axis to visualize the bell-shaped Gaussian curve.
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