- #1

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## Main Question or Discussion Point

Vibration Free

Please, are correct?

[tex]m \frac{d^2x}{dt^2} + kx = 0[/tex]

Where frequency is

[tex]w = \sqrt{\frac{k}{m}}[/tex]

[tex]\frac{d^2x}{dt^2} + \frac{k}{m}x = 0[/tex]

The characteristic equation is:

[tex]r^2 + w^2 = 0[/tex]

[tex]r = +or- iw[/tex] where [tex]i^2 = -1[/tex]

Then

[tex]x(t) = C_1e^{iwt} + C_2e^{-iwt}[/tex]

Calculating I can get

[tex]x(t) = a1cos(wt) + a2sin(wt)[/tex]

Now, I need to do to get the following equation. how do I find?

[tex]x(t) = Acos(wt - \delta)[/tex] (I think this is the equation we need to get the free vibration)

Please, are correct?

[tex]m \frac{d^2x}{dt^2} + kx = 0[/tex]

Where frequency is

[tex]w = \sqrt{\frac{k}{m}}[/tex]

[tex]\frac{d^2x}{dt^2} + \frac{k}{m}x = 0[/tex]

The characteristic equation is:

[tex]r^2 + w^2 = 0[/tex]

[tex]r = +or- iw[/tex] where [tex]i^2 = -1[/tex]

Then

[tex]x(t) = C_1e^{iwt} + C_2e^{-iwt}[/tex]

Calculating I can get

[tex]x(t) = a1cos(wt) + a2sin(wt)[/tex]

Now, I need to do to get the following equation. how do I find?

[tex]x(t) = Acos(wt - \delta)[/tex] (I think this is the equation we need to get the free vibration)