1983 Exam Question w/SHM and conservation of momentum

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The discussion revolves around a physics problem involving a block on a frictionless table attached to a spring and a second block colliding with it. The conservation of momentum is applied to determine the speed of the blocks after impact, yielding a result of 2/3Vo. For the period of simple harmonic motion, the formula T = 2π√(m/k) is used, with the mass being 3M. The main challenge lies in calculating the maximum compression of the spring, where kinetic energy is equated to potential energy, confirming that the approach of using initial kinetic energy to find x is correct. The transformation of kinetic energy into potential energy of the spring is emphasized as the key concept.
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A block of mass M is resting on a horizontal, frictionless table and is attached to a relaxed spring of spring constant k. A second block of mass 2M and initial speed vo collides with and sticks to the first block. Develop expressions for the following quantities in terms of M, k, and Vo.

a) v, the speed of the blocks immediately after impact
b) x, the maximum distance the spring is compressed
c) T, the period of the subsequent simple harmonic motion




m1v1+m2v2=m1v1'+m2v2'
EPE=.5kx2
KE = .5mv2
T = 2pi*sqrt(m/k)




I'm only having trouble with part b. I knew to use conservation of momentum for a and get 2/3vo. c was easy as you could just use the last equation and plug in 3M and k. But for b I'm not sure if I'm doing it right. What I'm doing it plugging in 3M and 2/3vo to solve for the initial KE and setting it equal to .5kx2 to get x. Is this right?
 
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Looks right to me. All that's happening is the kinetic energy of the blocks is transforming into the potential energy of the spring.
 

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