- #1
bob tran
- 17
- 0
Homework Statement
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. Homework Equations
[tex]
T=2\pi \sqrt{\dfrac{m}{k}}\\
\dfrac{1}{2}mv^2=\dfrac{1}{2}kA^2
[/tex]
The Attempt at a Solution
[tex]
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}
[/tex]