Have the answer (in red) just need help working it out please. Question 16 A 2.0

Question

Have the answer (in red) just need help working it out please. Question 16

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 oscillation that result from this collision? A. 0.300 m, 1.26 s B. 0.300 m, 0.889 s C 0.424 m, 0.889 s D. 0.424 m, 1.26 s E. 0.424 m, 5.00 s

Explanation / Answer

since the collision happens by the conservation of momemtum

2(3) + 0 = 4(v)

v = 1.5 m/sec is the common velocity for 4kg block formed

now by the conservation of energy we get (0.5*4*(1.5^2)) = (0.5*100*A^2)

A = ((0.5*4*(1.5^2))/50)^0.5

A = 0.3 m

time period T = 2pi/w

where K = mw^2

100 = 4w^2

w = 5

T = 6.28/5

T = 1.26 sec

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