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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? 0.300 m, 1.26 s 0.424 m, 5.00 s 0.424 m, 0.889 s 0.300 m, 0.889 s 0.424 m, 1.26 s

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MathPhys

Answer:

0.424 m, 1.26 s

Explanation:

The initial kinetic energy = the final stored energy in the spring

1/2 m v² = 1/2 k x²

x = √(m v² / k)

x = √(2.00 kg * (3.00 m/s)² / 100 N/m)

x ≈ 0.424 m

The angular frequency of the spring is:

ω = √(k / m)

ω = √(100 N/m / (2.00 kg + 2.00 kg))

ω = 5.00 rad/s

Period is:

f = 2π / ω

f = 2π / (5.00 rad/s)

f ≈ 1.26 s

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