College Physics question, Help ASAP?

Question

A 2.0kg mass is traveling at 5.0 m/s on a smooth horizontal surface when it collides with and sticks to a stationary 6.0 kg mass. The larger mass is attached to a light spring of force constant 150 N/m. Find (a) the amplitude of the resulting oscillations of this system (b) the frequency and (c) the period of the oscillations.

This is the exact question that I have, there was no drawing formulas or other info provide to answer this question. Please help I need to know how to answer this question because it will be on a Exam.

Can you show how to work it out? I don't just need the answer, I need to show the work.

Answer 1

a)
InitialEnergy = 0.5*m1*v1^2
FinalEnergy = 0.5*k*Amplitude^2
Amplitude = SquareRoot(6.6666)

b) f = 2 pi * SquareRoot(k/TotalMass) k = spring constant, f = frequency.

c) P = 1/f P= period, by definition.

Answer 2

You can't initially use conservation of energy to do this problem, as it's an inelastic collision (the masses stick together) and energy is lost to heat. You need to use conservation of momentum:

mv = (m + M)V where little m is little mass, etc. big V is velocity of the two masses stuck together. Now, you can use energy:

(1/2)(m + M)V^2 = (1/2)(mv)^2/(m + M) = 1/2kx^2

to get x, the amplitude of the osc.

Thus

a) x = mv*(k(m+M))^(-1/2)

b) w = (k/(m + M))^(1/2)
f = w/(2pi)

c) T = 1/f

Answer 3

The answer is 4.