- #1
danielu13
- 67
- 0
So, simple harmonic motion without damping is described generally by
[itex]x(t) = Acos(\omega*t +\delta)[/itex]
Which is derived from the differential equation
[itex]x''+\frac{k}{m}x = 0[/itex]
We know that
[itex] A = \sqrt{c_1^2+c_2^2}[/itex]
and
[itex]tan\delta = \frac{c_1}{c_2}[/itex]
With the differential equation, dealing with an initial condition is relatively easy, but it does not work as easily if using the generalized equation. Is there a way of making a relationship between [itex]A[/itex] and [itex]\delta[/itex]? I've worked with the equations a bit and can't find anything, but thought someone on here might know something different.
[itex]x(t) = Acos(\omega*t +\delta)[/itex]
Which is derived from the differential equation
[itex]x''+\frac{k}{m}x = 0[/itex]
We know that
[itex] A = \sqrt{c_1^2+c_2^2}[/itex]
and
[itex]tan\delta = \frac{c_1}{c_2}[/itex]
With the differential equation, dealing with an initial condition is relatively easy, but it does not work as easily if using the generalized equation. Is there a way of making a relationship between [itex]A[/itex] and [itex]\delta[/itex]? I've worked with the equations a bit and can't find anything, but thought someone on here might know something different.