Model No:SPH-M012
Aim: Study the stated oscillatory system and determine the relevant period, frequency, coupling or mechanical parameter.
Product: To determine The coefficient of damping K , To determine Relaxation time t , To determine The quality factor Q of a damped simple harmonic motion using a simple pendulum
The Damped Simple Harmonic Motion Apparatus Using a Simple Pendulum is designed for physics laboratory experiments to study damping in oscillatory motion and determine the coefficient of damping (K), relaxation time (T), and quality factor (Q). The apparatus demonstrates how the amplitude of a pendulum gradually decreases due to energy dissipation during oscillation.
By observing the decay in amplitude over successive oscillations and recording the corresponding time intervals, students can analyze the damping characteristics and calculate important parameters of damped simple harmonic motion. The experiment helps explain energy loss, damping effects, relaxation time, and the relationship between damping and the quality factor of an oscillating system.
This educational apparatus is suitable for physics laboratories in colleges, universities, and engineering institutions. It supports practical learning in oscillations, mechanical damping, energy dissipation, and experimental physics.
To determine The coefficient of damping K , To determine Relaxation time t , To determine The quality factor Q of a damped simple harmonic motion using a simple pendulum
To determine the following dynamic properties of a lightly underdamped simple pendulum:
Specifications:
Contents:
Step-by-Step Data Analysis
Step A: Finding the Slope By plotting Time (t) on the X-axis and log10(An ) on the Y-axis, a perfect linear regression yields a negative slope:
Slope = ? log10(An ) / ?t = (0.5658 - 1.0000) / (50.0 - 0.0) = -0.008684 s-1
Step B: Calculating Damping Coefficient (K)
K = -2.303 • Slope = -2.303 • (-0.008684) = 0.020 s-1
Step C: Calculating Relaxation Time (?)
? = 1 / K = 1 / 0.020 = 50.0 seconds
Interpretation: It takes exactly 50 seconds for the amplitude to drop to 1/e (~36.8%) of its initial value.
Step D: Calculating Quality Factor (Q) Q = 2 • ? • ? / T = (2 • 3.14159 • 50.0) / 2.0 = 157.08
Interpretation:
The high Q-factor (157.08) confirms that the system is lightly damped, executing many oscillations before losing its energy.
