Model No:SPH-M039
Determine the acceleration due to gravity using a simple pendulum and plot T_ against length
To determine the acceleration due to gravity (g), a simple pendulum is set into motion at a small angle to measure its time period (T) across various effective lengths (L). The relationship is governed by the formula:
T = 2? * sqrt(L / g) => T² = (4?² / g) * L
Contents:
1. Clamp stand
2. a split cork
3. a heavy metallic (brass/iron) spherical bob with a hook
4. a long, fine, strong cotton thread/string (about 2.0 m)
5. stop-watch
To determine the acceleration due to gravity (g), a simple pendulum is set into motion at a small angle to measure its time period (T) across various effective lengths (L). The relationship is governed by the formula:
T = 2? * sqrt(L / g) => T² = (4?² / g) * L
Theoretical Background
The primary objective of this experiment is to determine the acceleration due to gravity (g) using a simple pendulum. A simple pendulum consists of a small, dense metallic mass (referred to as the bob) suspended from a rigid, frictionless pivot point by a light, inextensible string of length L. When displaced from its central equilibrium position by a small angle, the pendulum executes oscillatory motion under the influence of gravity.
For small angular displacements (typically ? ? 10°), the restoring force acting on the bob is directly proportional to its displacement but directed opposite to it. Under this specific condition, the motion closely approximates Simple Harmonic Motion (SHM). The time period (T) of a simple pendulum—representing the time taken to complete one full oscillation—is governed by the formula:
T = 2? * ?(L / g)
Squaring both sides of this equation yields a linear relationship suitable for graphical analysis:
T² = (4?² / g) * L
Contents:
1. Clamp stand
2. a split cork
3. a heavy metallic (brass/iron) spherical bob with a hook
4. a long, fine, strong cotton thread/string (about 2.0 m)
5. stop-watch
The equation of a straight line is y = mx. Comparing this to our squared pendulum formula T² = (4?² / g) * L reveals that the slope (m) of the graph is:
Slope = ?T² / ?L = 4?² / g
Rearranging the formula allows us to isolate and solve for g:
g = 4?² / Slope
Using the slope calculated from the ideal graph trendline (Slope = 4.024 s²/m):
g = [4 * (3.1416)²] / 4.024
g = 39.4784 / 4.024
g ? 9.81 m/s²
Conclusion: The experimentally derived acceleration due to gravity is approximately 9.81 m/s².
Experimental Methodology
To systematically evaluate this relationship and extract an accurate value for g, the following experimental sequence is performed:
