Various Aspects of Harmonic Motion Using a Driven Harmonic Motion Analyzer
CURTIN UNIVERSITY OF TECHNOLOGY
DEPARTMENT OF APPLIED PHYSICS
Physical Measurement 201
DRIVEN HARMONIC OSCILLATOR
Abstract
The purpose of this experiment is to investigate the various aspects of harmonic motion using a Driven Harmonic Motion Analyser (DHMA). The aspects that are investigated in this experiment is the spring constant k of two springs, the resonant frequency, the damping factor, and the relationship between phase and resonant frequency. The value of k of the first string by calculating the mean is (12.51 ± 0.001) N/m and the value of k by using linear regression is (12.7 ± 0.3) N/m. The value of k of the second string by calculating the mean is (9.79 ± 0.001) N/m and the value of k calculated using linear regression is (9.1 ± 0.5) N/m. The damping coefficient caused by magnet is (0.021 ± 0.001) Ns/m. The value of resonant frequency using spring 2 with no mass added is (2.1 ± 0.1) Hz, this value is obtained from looking at the maximum amplitude, the other values obtained from calculation and looking at the phase are 2.05 Hz and (2.5 ± 0.1) Hz.
Experiment Conducted:
27th April 2004
AIM
General:
- Investigate various aspects of harmonic motion using a driven harmonic motion analyser
Specific: - Measure the spring constant k for two springs - Measure the resonant frequency - Investigate the effect of damping on the period of the oscillation, and to determine the damping coefficient b - To investigate the relationship between the phase and resonant frequency.
EQUIPMENT - Driven harmonic motion analyser - Computer interface - Additional masses (0.01 kg each) - Magnetic damping unit - 2 Springs - Meter ruler
INTRODUCTION
Consider a mass attached to a spring, damped and oscillated with external force as seen on the following diagram:
[pic]
Figure 1. Mass attached to a spring with constant k and it is damped with a
DEPARTMENT OF APPLIED PHYSICS
Physical Measurement 201
DRIVEN HARMONIC OSCILLATOR
Abstract
The purpose of this experiment is to investigate the various aspects of harmonic motion using a Driven Harmonic Motion Analyser (DHMA). The aspects that are investigated in this experiment is the spring constant k of two springs, the resonant frequency, the damping factor, and the relationship between phase and resonant frequency. The value of k of the first string by calculating the mean is (12.51 ± 0.001) N/m and the value of k by using linear regression is (12.7 ± 0.3) N/m. The value of k of the second string by calculating the mean is (9.79 ± 0.001) N/m and the value of k calculated using linear regression is (9.1 ± 0.5) N/m. The damping coefficient caused by magnet is (0.021 ± 0.001) Ns/m. The value of resonant frequency using spring 2 with no mass added is (2.1 ± 0.1) Hz, this value is obtained from looking at the maximum amplitude, the other values obtained from calculation and looking at the phase are 2.05 Hz and (2.5 ± 0.1) Hz.
Experiment Conducted:
27th April 2004
AIM
General:
- Investigate various aspects of harmonic motion using a driven harmonic motion analyser
Specific: - Measure the spring constant k for two springs - Measure the resonant frequency - Investigate the effect of damping on the period of the oscillation, and to determine the damping coefficient b - To investigate the relationship between the phase and resonant frequency.
EQUIPMENT - Driven harmonic motion analyser - Computer interface - Additional masses (0.01 kg each) - Magnetic damping unit - 2 Springs - Meter ruler
INTRODUCTION
Consider a mass attached to a spring, damped and oscillated with external force as seen on the following diagram:
[pic]
Figure 1. Mass attached to a spring with constant k and it is damped with a
References: PASCO scientific, 1986, Instruction Manual and Experiment Guide for the PASCO Scientific Model ME-9210A, Roseville, CA, USA Pain, H.J. 2000, 5th edition, The Physics of Vibrations and Waves, John Wiley & Sons Limited, Chichester, UK