- Summary
- What is the meaning of the x variable in the equation for damping force in respect of non-driven, damped oscillations?

Hi,

for ease of reference this posting is segmented into :

Regarding (one, linear, second-order, homogeneous, ordinary, differential) equation describing the force in a non-driven, damped oscillation:

F = m.a = -k.x - b.v

F = m.(d^2.x/dt^2) = -k.x - b(dx/dt)

Rearranging:

m.(d^2.x/dt^2) + k.x + b(dx/dt) = 0

...

(d^2.x/dt^2) + b/m(dx/dt) + k/m.x = 0

But x in k/m.x and dx/dt are in respect of x1= f(t) for simple harmonic oscillation while x in d^2.x/dt^2 and d^2.x/dt^2 is in respect of equation x2 = f(t) for damped oscillation.

So there are in fact variables x1 and x2 but they are both x in the equation (and treated as such).

How can this be correct?

--

Apologies for unicode. Thanks for bearing with me.

Regards

PG

for ease of reference this posting is segmented into :

**1. Background**

2. Focus

3. Question

1. Background:2. Focus

3. Question

1. Background:

Regarding (one, linear, second-order, homogeneous, ordinary, differential) equation describing the force in a non-driven, damped oscillation:

F = m.a = -k.x - b.v

F = m.(d^2.x/dt^2) = -k.x - b(dx/dt)

Rearranging:

m.(d^2.x/dt^2) + k.x + b(dx/dt) = 0

...

(d^2.x/dt^2) + b/m(dx/dt) + k/m.x = 0

**2. Focus:**But x in k/m.x and dx/dt are in respect of x1= f(t) for simple harmonic oscillation while x in d^2.x/dt^2 and d^2.x/dt^2 is in respect of equation x2 = f(t) for damped oscillation.

**3. Question:**So there are in fact variables x1 and x2 but they are both x in the equation (and treated as such).

How can this be correct?

--

Apologies for unicode. Thanks for bearing with me.

Regards

PG