How can conservation of energy be applied to solve a spring collision problem?

[freshcoast]

Homework Statement

Homework Equations

http://en.wikipedia.org/wiki/Simple_harmonic_motion

The Attempt at a Solution

So I labeled the image at the points of interest where I would need to calculate certain values.

for part a)
so from A --> B
All I'm trying to figure out here is how fast the object is going before collision,
using conservation of energy I am able to the final velocity of the object by finding the change in potential energy.

B -- > C
Since it is a perfectly inelastic collision, I would know that momentum is conserved which will lead me to find the final velocity the combined object is going after collision, with that using momentum conservation laws,

mV_o = (m + 4m)V_f

C -- > D
again, conservation of energy is applied but this time with potential spring energy, which I have set up as,

KE_initial = PE_springF

Since I have found the velocity, all I am solving for is X which would equal to the amplitude(A) that the spring undergoes. Once I have found that, I know that the general term for position as a function of time in a harmonic system is

x(t) = Acosθ

part b)

I need a clue on this one, Am I to just compare the initial potential energy of mass m to the potential spring energy?

 

[TSny]

Look's good to me. But, you would still want to express θ in cosθ as an explicit function of time. Also, if you choose t = 0 to be the time of the collision with the spring, then you might think about whether or not to use the sine function instead of cosine.

For part b, you should be able to express your answer as a simple numerical fraction.

 

[Simon Bridge]

For part (a) you were asked to find $x(t)$ and you have found $x(\theta)$.
Fr part (b) you are correct - you have an expression for the gravitational potential energy, and you have an expression for the energy stored in the spring. The "fraction" is one divided by the other.