Simple Harmonic Motion on an air track

[CloCon]

Homework Statement

A 0.20-kilogram mass is sliding on a horizontal, frictionless air track with a speed of 3.0 meters per second when it instantaneously hits and sticks to a 1.3-kilogram mass initially at rest on the track. The 1.3-kilogram mass is connected to one end of a massless spring, which has a spring constant of 100 Newtons per meter. The other end of the spring is fixed.

Homework Equations

F = -kx
KE = 1/2m(v)squared
momentum = mass x velocity

The Attempt at a Solution

The first couple parts of the problem ask you to solve for the linear momentum and kinetic energy of the masses before and immediately after collision. I interpreted "immediately after the impact" to indicate that I'm supposed to calculate the linear momentum/KE of the masses without taking the spring into account.

a. momentum before impact = 0.6 kg m/s
KE before impact = 0.9 Joules
b. momentum after impact = 0.6 kg m/s
KE after impact = 0.3 J

c. Determine the amplitude of the harmonic motion.
d. Determine the period of the harmonic motion.

I don't really know where to start on parts C and D- I thought to use F=mA to determine the spring force (F=-kX) needed to stop the motion of the mass since the k value is provided (100 n/m), but there's no A value to plug into F=mA. I suspect that KE initial + PE initial = KE final + PE final might factor in because at maximum amplitude PE = 0.3 J, but I don't know where. How might I solve this?

EDIT:

Took another crack at it; am I on the right track?

PE final = 0.3 Joules
PE = (1/2)k(x)squared
0.3 J= (1/2)*(100 N/m)*x squared
x = .0015 m
Would that be the amplitude? If so, how might I find the period?

EDIT 2:

Went Wikipedia hunting and came up with the formula T = 2pi ROOT(m/k). Plugged in all the numbers and came out with .76 seconds. I haven't a clue if that formula applies for a mass on an air track as it applies for a hanging mass, though, so please tell me whether I've got it right or all wrong.

In case you're curious, this problem is from the 1995 Physics AP free response section.

 

[diazona]

Are you sure about that 0.3J for final kinetic energy? I get something different...

EDIT:

Took another crack at it; am I on the right track?

PE final = 0.3 Joules
PE = (1/2)k(x)squared
0.3 J= (1/2)*(100 N/m)*x squared
x = .0015 m
Would that be the amplitude?

That is the right procedure for finding the amplitude.

EDIT 2:

Went Wikipedia hunting and came up with the formula T = 2pi ROOT(m/k). Plugged in all the numbers and came out with .76 seconds. I haven't a clue if that formula applies for a mass on an air track as it applies for a hanging mass, though, so please tell me whether I've got it right or all wrong.

That formula applies for any mass attached to a spring, whenever the sum of all other forces on the mass (except for the spring force) is a constant. (Zero is a constant, of course)

 

[CloCon]

Thanks for the confirmation on the amplitude and period, diazona. I redid the calculation and discovered that I'd neglected to square the velocity to find KE- is this more in line with your calculations?

Momentum final = mV
0.6 kg m/s = 1.5 kg * v
V final = 0.4 m/s

KE final = 1/2 (mass 1 + mass 2) * Vf squared
KE final = 1/2 (1.5 kg) * (0.4 m/s)^2
KE final = .12 Joules