A horizontal massless spring has spring constant k , and a mass M is attached to

Question

A horizontal massless spring has spring constant k , and a mass  M is attached to its end. You pull it back a distance  x0 and give it a push such that it starts moving with speed v0 .

Part A

What is the total initial energy the spring has? Express your answer in terms of variables given in the problem.

1/2Mv0^2+1/2kx0^2

Correct

Part B

What is the amplitude of the oscillations the mass makes? Express your answer in terms of variables given in the problem.

2Ek

Part C

What is the maximum speed the mass has as it is oscillating? Express your answer in terms of variables given in the problem.

Part D

Right at the moment the mass has this maximum velocity, a smaller lump of mass  m lands on it. What is the speed of the mass with the lump on it, immediately after the lump lands? Express your answer in terms of quantities given in the problem, including m .

Part E

What is the amplitude of the oscillations of the mass  M with the lump  m on it? Again express your answer in terms of quantities given in the problem, including m .

I have attempted the other parts but other parts but cannot find the correct answer, please help

1/2Mv0^2+1/2kx0^2

Explanation / Answer

part B:

maximum amplitude is at the extreme point where total energy is in the spring and velocity is 0

so 1/2*k* A2 = 1/2Mv0^2+1/2kx0^2 = E

so A = sqrt(2E/k)

part c :

maximum speed is at the point where total energy is in the mass KE and x=0

so 1/2*M*v^2 = E

so V max = sqrt(2E/M)

part d:

when mass m dumps on it... the energy is still conserved and hence

1/2 * M * Vmax^2 = 1/2* (M+m)*Vnew^2

so Vnew = sqrt ( M/(M+m) ) * Vmax = sqrt (2E / (M+m) )

part E: 1/2*k*Anew^2 = E since the energy will be conserved... so Anew = sqrt(2E / k)

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