Solving Oscillation Problem: Frequency, Amplitude, Phase

[vande060]

Homework Statement

A mass m1 connected to a spring of force constant k
is at rest at equilibrium at the origin. It is struck inelastically
by a mass m2 moving at speed v0 at t = 0. Find
the frequency, amplitude and phase of the resulting simple
harmonic motion

Homework Equations

x(t) = A sin(ωt − theta)

freq = (B/A)^-1/2

The Attempt at a Solution

well, first off it is an inelastic collision so the masses will stick together so i think velocity should look like this after the collision

m1v0 = (m1 + m2)v1

v1 = (m1v0)/(m1 + m2)

then i went along with an equation for energy, i don't feel too good about this step

E = 1/2(m1 + m2)v1 + 1/2kx^2

freq = (B/A)^-1/2

freq = [k/(m1 + m2)]^-1/2

so then would i plug the amplitude(A) and the frequency(w) into the equation x(t) from above

i will be amazed if this is even close. help please.

 

[rock.freak667]

I agree with your ω=√[k/(m₁+m₂)]

You found v₁, so when t=0, v(0)=v₁ which should help you get A.

and x(0)= 0 to get θ.