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WY

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I'm attempting this question and I'm wondering if this is the correct way of going about it or if I'm completely off track:

For lunch you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.300 kg of Italian ham. The slices of ham are weighed on a plate of mass 0.400 kg placed atop a vertical spring of negligible mass and force constant of 200 N/m. The slices of ham are dropped on the plate all at the same time from a height of 0.250 m. They make a totally inelastic collision with the plate and set the scale into vertical simple harmonic motion (SHM). You may assume that the collision time is extremely small.

What is the amplitude of oscillation A of the scale after the slices of ham land on the plate?

What is the period of oscillation T of the scale?

I started using conservation of GPE and equating it to the energy of the spring

mgh = 1/2*k*A^2

and made A the subject to find the amplitude - would this give me the right answer?

And then for the second part I used (2*pi)/sqrt(k/m)=T and m = the mass of ham - should i include the mass of the plate?

thanks in advance!