# Amplitude and Period of Oscillation from Collision

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1. Dec 13, 2015

### bob tran

1. The problem statement, all variables and given/known data
A 2.00-kg object is attached to an ideal massless horizontal spring of spring constant 100.0 N/m and is at rest on a frictionless horizontal table. The spring is aligned along the x-axis and is fixed to a peg in the table. Suddenly this mass is struck by another 2.00-kg object traveling along the x-axis at 3.00 m/s, and the two masses stick together. What are the amplitude and period of the oscillations that result from this collision?
Correct Answer: A=0.300 m, T=1.26 s

2. Relevant equations

$$T=2\pi \sqrt{\dfrac{m}{k}}\\ \dfrac{1}{2}mv^2=\dfrac{1}{2}kA^2$$
3. The attempt at a solution
$$m=2 + 2 = 4 \ \texttt{kg}\\ \dfrac{1}{2}mv^2=\dfrac{1}{2}kA^2\\ A=\sqrt{\dfrac{mv^2}{k}}\\ A=\sqrt{\dfrac{(4)(3)^2}{100}}=0.600 \ \texttt{m}\\ T=2\pi \sqrt{\dfrac{m}{k}}\\ T=2\pi \sqrt{\dfrac{4}{100}}\\ T=1.26 \ \texttt{s}$$

2. Dec 13, 2015

### JeremyG

What is the speed of the combined mass after the collision? Is it still 3m/s?

3. Dec 13, 2015

### bob tran

Thanks!
$$v=\dfrac{m_1 v_1 + m_2 v_2}{m_1 + m_2} = 1.5 \dfrac{\texttt{m}}{\texttt{s}}\\ A=\sqrt{\dfrac{(4)(1.5)^2}{100}}=0.300 \ \texttt{m}$$