Finding the Effective Mass and Spring Constant of a Force Probe from Simple Harmonic Motion

The simple harmonic motion of a spring-mass system generally exhibits a behavior strongly influenced by the geometric parameters of the spring. In this paper, we study the oscillatory behavior of a spring-mass system, considering the influence of varying the average spring diameter Φ on the elastic constant k, the angular frequency ω, the damping factor γ, and the dynamics of the oscillations. It was found that the elastic constant k is proportional to Φ-3, while the natural frequency ω0 is proportional to Φ- 3 / 2, and γ decreases as Φ increases. We also show the differences obtained in the value of the angular frequency ω when the springs are considered as ideal (massless), taking into account the effective mass of the spring, and considering the influence of the damping of the oscillations. This experiment provides students with the possibility of understanding the differences between theoretical models that include well-known corrections to determine the frequency of oscillations of a spring-mass system.

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Error analysis of initial angle for simple harmonic motion in science experiment education

Journal of educational Research Institute ◽

10.15564/jeju.2017.11.19.2.155 ◽

2017 ◽

Vol 19 (2) ◽

pp. 155-167

Author(s):

Se-Hun Kim

Keyword(s):

Error Analysis ◽

Initial Angle ◽

Harmonic Motion ◽

Simple Harmonic Motion

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TPT NOTES: Damped Simple Harmonic Motion on a Linear Air Track

The Physics Teacher ◽

10.1119/1.2352550 ◽

1969 ◽

Vol 7 (7) ◽

pp. 395-396

Author(s):

Thomas B. Greenslade

Keyword(s):

Harmonic Motion ◽

Simple Harmonic Motion

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Response characteristics of electromagnetic seismographs and their dependence on the instrumental constants

Bulletin of the Seismological Society of America ◽

10.1785/bssa0390030205 ◽

1949 ◽

Vol 39 (3) ◽

pp. 205-218

Author(s):

S. K. Chakrabarty

Keyword(s):

General Solution ◽

Equation Of Motion ◽

Harmonic Motion ◽

Response Characteristics ◽

Local Earthquakes ◽

Simple Harmonic Motion ◽

The Earth ◽

Electromagnetic Seismograph ◽

Different Types ◽

Proper Values

Summary The equation of motion of the seismometer and the galvanometer in an electromagnetic seismograph has been derived in the most general form taking into consideration all the forces acting on the system except that produced by hysteresis. A general solution has been derived assuming that the earth or the seismometer frame is subjected to a sustained simple harmonic motion, and expressions for both the transient and the steady term in the solution have been given. The results for the particular case when the seismograph satisfies the Galitzin conditions can easily be deduced from the results given in the present paper. The results can now be used to study the response characteristics of all electromagnetic seismographs, whether they satisfy the Galitzin conditions or not, and will thus give an accurate theoretical picture of the response also of seismographs used for the study of “local earthquakes” and “microseisms” which do not in general obey the Galitzin conditions. The results obtained can also be used to get analytically the response of the seismographs for different types of earth motion from the very beginning, and not only after the transient term has disappeared. The theory of the response to simple tests used to determine the dynamic magnification of any seismograph and also to determine and check regularly the instrumental constants of the seismographs has been worked out. The results obtained can also be used for ascertaining the proper values of the instrumental constants suitable for the various purposes for which the seismographs are to be used.

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