# Finding the total response of an undamped spring mass system

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1. Oct 2, 2016

### whitejac

1. The problem statement, all variables and given/known data

2. Relevant equations
The response of a spring mass system can be simplified to equal:
x(t) = (x0 - (F0 / (k - mω2))cos(ωnt) + (x'/ωn)sin(ωnt) + (F0 / (k - mω2))cos(ωt)

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

ωn = √(k/m)

3. The attempt at a solution
Given normal initial conditions, x = x' = 0

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

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

2. Oct 3, 2016

### Simon Bridge

No. Those are arbitrarily supplied by an external agency.

3. Oct 3, 2016

### whitejac

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.

4. Oct 3, 2016

### 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.