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Pendulum Gravity Formula:
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The pendulum gravity formula calculates the acceleration due to gravity (g) using the length of a pendulum (L) and its period of oscillation (T). This method provides a simple way to measure gravitational acceleration using pendulum motion.
The calculator uses the pendulum gravity formula:
Where:
Explanation: The formula derives from the relationship between a pendulum's physical characteristics and its oscillatory motion under Earth's gravity.
Details: Measuring gravitational acceleration is fundamental in physics and engineering, helping us understand planetary characteristics, validate physical laws, and calibrate scientific instruments.
Tips: Enter the pendulum length in meters and oscillation period in seconds. For accurate results, ensure precise measurements of both parameters.
Q1: What is the standard value of Earth's gravity?
A: The standard value is approximately 9.80665 m/s², though it varies slightly depending on location and altitude.
Q2: How accurate is the pendulum method?
A: With careful measurement of length and period, the pendulum method can provide gravity measurements accurate to within 0.1-0.5%.
Q3: What affects the accuracy of pendulum measurements?
A: Factors include air resistance, amplitude of swing, string mass, pivot friction, and measurement precision of length and time.
Q4: Can this formula be used for any pendulum?
A: The formula works best for simple pendulums with small oscillation angles (less than 15 degrees) where the motion approximates simple harmonic motion.
Q5: Why is π² used in the formula?
A: The π² term comes from the mathematical derivation of the pendulum period formula from the principles of simple harmonic motion.