A 12.5 kg mass is traveling to the right with a speed of 2.40 m/s on a smooth ho

Question

A 12.5 kg mass is traveling to the right with a speed of 2.40 m/s on a smooth horizontal surface when it collides with and sticks to a second 12.5 kg mass that is initially at rest but is attached to a light spring with force constant 120 N/m

1) Find the frequency of the subsequent oscillations.

2)Find the amplitude of the subsequent oscillations.

3)Find the period of the subsequent oscillations.

4)How long does it take the system to return the first time to the position it had immediately after the collision?

Explanation / Answer

Here ,

mass , m= 12.5 Kg

initial speed , u = 2.4 m/s

force constant , k = 120 N/m

1)

Frequency , f = (1/2pi) * sqrt(k/m)

Frequency , f = 1/(2*pi) * sqrt(120/(12.5 + 12.5))

Frequency , f = 0.349 Hz

the frequency of the subsequent oscillations is 0.349 Hz

2)

let the speed after collision is v

using conservation of momentum

(12.5 + 12.5) * v = 12.5 * 2.4

v = 1.2 m/s

let the amplitude of A

0.5 * 120 * A^2 = 0.5 * 25 * 1.2^2

A = 0.55 m

the amplitude is 0.55 m

3)

period = 1/f

Period = 1/.349

Period = 2.9 s

the period of the subsequent oscillations is 2.9 s

4)

as time taken will be one period

T = 2.9 s

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