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## Homework Statement

A mass m1 is located on a platform with mass M. The platfrom is located on springs with total constant k such that it can swing vertically in direction x.

a) Write down the equations of motion assuming mass m1 will always be connected to the platform. Write it as x(t)

b) What's the maximum force on the spring?

c) What's the maximum normal force between m1 and M?

d) What's the Amplitude so that m1 will takeoff from the platform

Thanks in advance

## Homework Equations

$$m*\frac{d^2x}{dt^2} = -kx$$

## The Attempt at a Solution

a)

I have no information given, so I assume I can't use sin() or cos() or am I overthinking it?

Let m = m1+M

So we have $$m*\frac{d^2x}{dt^2} = -kx$$

And I use the Cauchy–Euler equation $$m*\lambda^2*e^{{\lambda}*t} + k*e^{{\lambda}*t}=0$$

Which leads to: $$\lambda_{1,2} = +-\sqrt{\frac{-k}{m}}$$

Here I have a minus inside the root. I think since no direction is given I can say that I only care about the absolute value

So I have $$A*e^{\sqrt{k/m}*t}+B*e^{-\sqrt{k/m}*t}$$

There is nothing more that I can do about the constants, because there is nothing given.

For b) and c) I know it has to be on the bottom dead center. d) The acceleration of the mass on the spring has to be greater than gravity

How do I continue from here? My ideas would be to solve it for ##\sqrt{k/m}## or use ##E_{pot} + E_{kin}## but it seems I'm totally off track.