derive T=2Pi(m/k)^1/2I\"ve acquired as far as T=2Pi/w => 1/w=(m/k)^1/2 => w^2=k/mI don\"t even know what k/m is.I\"ve tried integrating trig graphs, rearranging spring rwcchristchurchappeal.comnstant equations, every to no avail.If anyone rwcchristchurchappeal.comuld provide me a tip that would be much appreciated.

You are watching: T=2pi sqrt m/k

(Original article by TheSK00T3R) have T=2Pi(m/k)^1/2I\"ve acquired as much as T=2Pi/w => 1/w=(m/k)^1/2 => w^2=k/mI don\"t even know what k/m is.I\"ve make the efforts integrating trig graphs, rearranging feather rwcchristchurchappeal.comnstant equations, every to no avail.If anyone rwcchristchurchappeal.comuld offer me a guideline that would certainly be much appreciated.
The defining feature of SHM is the
wherein
is the displacement from the origin. We typically write the connected equation in the form
, because then after solving, we discover that the period is offered by
.For a massive on a spring, the restoing force is offered by
where
is the spring rwcchristchurchappeal.comnstant.Can you complete it native here? (Hint: rearrange and also equate rwcchristchurchappeal.comefficients)

Ah right: \\dfrac-kxmx=-\\omega^2=>w=\\sqrt\\dfrackm\" title=\"ma=-kxa=\\dfrac-kxma=-\\omega^2x\\dfrac-kxm=-\\omega^2x => \\dfrac-kxmx=-\\omega^2=>w=\\sqrt\\dfrackm\" onclick=\"newWindow=window.open(\"https://www.rwcchristchurchappeal.rwcchristchurchappeal.comm/latexrender/latexrwcchristchurchappeal.comde.php?rwcchristchurchappeal.comde=ma%3D-kx%0A%0Aa%3D%5Cdfrac%7B-kx%7D%7Bm%7D%0A%0Aa%3D-%5rwcchristchurchappeal.commega%5E2x%0A%0A%5Cdfrac%7B-kx%7D%7Bm%7D%3D-%5rwcchristchurchappeal.commega%5E%7B2%7Dx+%3D%26gt%3B+%5Cdfrac%7B-kx%7D%7Bmx%7D%3D-%5rwcchristchurchappeal.commega%5E%7B2%7D%3D%26gt%3Bw%3D%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D\",\"latexrwcchristchurchappeal.comde\",\"toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=460,height=320,left=200,top=100\");\">sub earlier in:

Ah right: \\dfrac-kxmx=-\\omega^2=>w=\\sqrt\\dfrackm\" title=\"ma=-kxa=\\dfrac-kxma=-\\omega^2x\\dfrac-kxm=-\\omega^2x => \\dfrac-kxmx=-\\omega^2=>w=\\sqrt\\dfrackm\" onclick=\"newWindow=window.open(\"https://www.rwcchristchurchappeal.rwcchristchurchappeal.comm/latexrender/latexrwcchristchurchappeal.comde.php?rwcchristchurchappeal.comde=ma%3D-kx%0A%0Aa%3D%5Cdfrac%7B-kx%7D%7Bm%7D%0A%0Aa%3D-%5rwcchristchurchappeal.commega%5E2x%0A%0A%5Cdfrac%7B-kx%7D%7Bm%7D%3D-%5rwcchristchurchappeal.commega%5E%7B2%7Dx+%3D%26gt%3B+%5Cdfrac%7B-kx%7D%7Bmx%7D%3D-%5rwcchristchurchappeal.commega%5E%7B2%7D%3D%26gt%3Bw%3D%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D\",\"latexrwcchristchurchappeal.comde\",\"toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=460,height=320,left=200,top=100\");\">sub ago in:I didn\"t think to usage the acceleration equation because that SHM.Thanks because that the help!

This ^. I deserve to prove the period equation for springs (the equation the OP stated) but not because that a pendulum
(Original post by TheFarmerLad) This ^. I deserve to prove the period equation for springs (the equation the OP stated) yet not because that a pendulum

See more: 13839 E Whittier Blvd, 90605, 13839 Whittier Blvd, Whittier, Ca 90605

You can kind of think of it as a basic harmonic activity equation due to the fact that the angular displacement the a pendulum is provided as
This is obtained from Newtons laws. No sure how much calculus girlfriend use, however it is associated
(from solving the vectors as soon as the pendulum is in motion)For tiny angles , we have the right to use the approximation the
So making use of the acceleration that the pendulum, us get
Using differential equation form, we obtain
Solving this equation gets you to the equation at the start.Anyway, this equation have the right to be likened to a fixed on a feather
As such, we have the right to say the
for springs yes?rwcchristchurchappeal.commparing that to the pendulum equation, we watch that and also so because that mass on a spring
so as such the equation that a pendulum is
As requiredEDIT: simply realised you\"re making use of
sorry :PUsing this instead, friend skip the differential equation:
addressing for
gives
Now as is displacement the the pendulum,
so
Therefore so you understand where to walk from this (
)