- #1

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So, because the force is not constant, the acceleration is also not constant..

How then can we apply Newton's second law: F = mass x acceleration to springs?

- Thread starter gkangelexa
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- #1

- 81

- 1

So, because the force is not constant, the acceleration is also not constant..

How then can we apply Newton's second law: F = mass x acceleration to springs?

- #2

WannabeNewton

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- #3

Matterwave

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[tex]F=-kx(t)=m\frac{d^2 x(t)}{dt^2}[/tex]

Which is a second order differential equation that we have to solve (we need 2 initial conditions to completely solve this).

- #4

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If you were to bring the mass on the spring to an initial displacement and let it go, you could figure out the position function x(t) by solving that differential equation:

[tex]x(t)=x_0~cos(\omega t+\phi )[/tex]

Where:

[tex]\omega^2=\frac{k}{m}[/tex]

- #5

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makes sense thanks!

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