A 2.00-kg object is attached to an ideal massless horizontal spring of spring co

Question

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 -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?

a) 0.424m,1.26s
b) 0.300m,1.26s
c) 0.424m,5.00s
d) 0.424m,0.889s
e) 0.300m,0.889s

Explanation / Answer

by momentum conservation

m1.V1 = (m1+m2).V2

2 x 3 = 4 x V2

V2 = 3/2 m/s

1/2.K.x2 = 1/2. (m1+M2).V22

1/2.100.x2 = 1/2 x 4 x 1.52

X = 0.3 m = amplitude

Now, velocity = V = .X

1.5 = x 0.3

= 5 rad/s

time period = 2.pi /

   = 2xpi / 5 = 1.26 se

hence option B

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