Vipul: /* Conclusion */

2011-08-14T00:50:49Z

Conclusion

← Older revision		Revision as of 00:50, 14 August 2011
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	===Conclusion===		===Conclusion===

	In this case, the block and spring execute [[simple harmonic motion]]. Note that the ''mean position'' is ''not'' the relaxed state of the spring, because of the role that the gravitational force on the ~~spring~~ plays in changing the equilibrium. Details about the oscillation are given below:		In this case, the block and spring execute [[simple harmonic motion]]. Note that the ''mean position'' is ''not'' the relaxed state of the spring, because of the role that the gravitational force on the block plays in changing the equilibrium. Details about the oscillation are given below:

	{\| class="sortable" border="1"		{\| class="sortable" border="1"

Vipul: Created page with "{{mechanics scenario}} In this article, we describe the following scenario. A block of mass $m$ is suspended vertically from a massless spring with spring constant
2011-08-13T01:53:03Z

Created page with "{{mechanics scenario}} In this article, we describe the following scenario. A block of mass <math>m</math> is suspended vertically from a massless spring with spring constant <m..."

New page
{{mechanics scenario}}

In this article, we describe the following scenario. A block of mass <math>m</math> is suspended vertically from a massless spring with spring constant <math>k</math>.

==Case that the spring is initially in its relaxed state==

===Conclusion===

In this case, the block and spring execute [[simple harmonic motion]]. Note that the ''mean position'' is ''not'' the relaxed state of the spring, because of the role that the gravitational force on the spring plays in changing the equilibrium. Details about the oscillation are given below:

{| class="sortable" border="1"
! Quantity !! Value
|-
| Displacement of mean position of oscillations from usual relaxed state of spring || <math>mg/k</math>
|-
| Amplitude of oscillation || Also <math>(mg)/k</math> (so the spring gets stretched by a maximum length of <math>(2mg)/k</math> and thus oscillates between its relaxed position and a stretched position of <math>(2mg)/k</math>.
|-
| Angular frequency <math>\omega</math> for oscillations || <math>\sqrt{k/m}</math>
|-
| Frequency of oscillations (number of oscillations per second) || <math>\frac{1}{2\pi} \sqrt{k/m}</math>
|-
| Time period of oscillation || <math>2\pi \sqrt{m/k}</math>
|}

==Other cases==

In general, the displacement of mean position from the usual relaxed state of the spring remains <math>mg/k</math> and the angular frequency, frequency of oscillations, and time period of oscillation remain the same. What ''can'' change is the amplitude of oscillations, which depends on the initial position and velocity of the system.