Solve questions on oscillations and kinetic energy

[SWoo]

A spring of spring constant k sits on a frictionless horizontal table, one end of the spring is attached to a wall the other end to a block of mass M= 2kg, also resting on the frictionless table. Another block of mass m=450g moving at a speed of 7m/s collides in-elastically with the block of mass M, as a result of the collision M moves in such a direction so as to compress the spring, which takes 0.4 seconds to reach maximum compression.

for a. what happens before removing M is that it oscillates alone and has separated from m. which is why now, you can remove M.
a. You now remove M when the system is at the point where v=0, How much time does it take for the mass M to go from having one third of its maximum kinetic energy to having 1/5 of its maximum kinetic energy as it is moving away form equilibrium.

doubling the mass doubles the energy so using the equation 1/2(2m)(v)^2=mv^2, you know that the Ek is changed by a factor of 2. however, apparently this is wrong. any ideas on how to solve it? to help solve the question, here are some hints:https://gyazo.com/2d8e1281d78037d5c8e0427075a23f00

b. The sphere of mass M and radius R shown rolls without slipping on the ground. It is attached at the top to a spring of spring constant k. The other end of the spring is attached to a wall. The system is in equilibrium, then you move the sphere by a small amount and the system goes into oscillation, find the period for small oscillations in terms of the quantities given.

I used this equation to solve the second part, but again, not getting the right answer. w0 = square root of mgR/I. Hints: https://gyazo.com/5d49cbb19ab59b85ec336f2205af7e23

c. A bar of length L is suspended from its top edge where it is free to rotate about the pivot, its bottom is connected to a horizontal spring of spring constant k the other end of the spring is connected to wall. Find the period of small oscillations for this bar.

used the same equation as b. hints: https://gyazo.com/d3b5f13dfed5554a037d0767977b8389

 

[BvU]

Hi again and again,

We still want some effort from you: there's no point in robbing you of the exercise by doing it for you. And to help you work through we need to know what you can muster yourself so we can try to be effective in nudging you towards understanding.

 

[haruspex]

You now remove M

Do you mean remove m?

what happens before removing M is that it oscillates alone and has separated from m. which is why now, you can remove M.

Assuming you mean remove m, it says to remove it when the velocity of the masses first reaches zero, not the second time it reaches zero.

doubling the mass

I see no mention of doubling a mass.

First step is to figure out the velocity of the masses just after impact.

For b and c, please post a separate thread for each independent question. You should fill in the template, showing any relevant standard equations or principles, and, as BvU says, show some attempt.