Finding the total response of an undamped spring mass system

[whitejac]

Homework Statement

Homework Equations

The response of a spring mass system can be simplified to equal:
x(t) = (x₀ - (F₀ / (k - mω²))cos(ω_nt) + (x'/ω_n)sin(ω_nt) + (F₀ / (k - mω²))cos(ωt)

where
x & x' are the initial conditions
ω is the exciting frequency
ω_n is the natural frequency
k is the spring constant
m is the mass
and F₀ is the amplification of the applied force

ω_n = √(k/m)

The Attempt at a Solution

Given normal initial conditions, x = x' = 0

x(t) = - (F₀ / (k - mω²))cos(ω_nt) + (F₀ / (k - mω²))cos(ωt)

and ω_n = √(k/m) = 6.325rad / s
Is there a way to solve for F₀ and ω?

 

[Simon Bridge]

No. Those are arbitrarily supplied by an external agency.

 

[whitejac]

No. Those are arbitrarily supplied by an external agency.

That's what I thought but someone said you could by substituting the given f (t) with the f (t) for harmonic motion - but it seemed like I still on had one one equation 2 unknowns so it didn't seem possible.

 

[rude man]

There are three terms in your "relevant equation". Which one or ones look like they could be affected by gravity alone? Remember initial conditions = 0.