A750 g air-track glider attached to a spring with spring constant 14.0 n/m is sitting at rest on a frictionless air track. a 200 g glider is pushed toward it from the far end of the track at a speed of 170 cm/s . it collides with and sticks to the 750 g glider. what are the amplitude and period of the subsequent oscillations?

the amplitude of  the subsequent oscillations is 0.11  m

the period of the subsequent oscillations is 1.94 s

Explanation:

given Information:

the mass of air-track glider, = 750 g = 0.75 kg

spring constant, k = 13.0 N/m

the mass of glider, = 200 g = 0.2 kg

the speed of glider,   = 170 cm/s = 1.7 m/s

the amplitude of  the subsequent oscillations is A = 0.11  m

according to mechanical enery equation, we have

where

A is the amplitude and   is the final speed.

to find , we can use momentum conservation lwa, where the initial momentum is equal to the final momentum.

= 0, thus

(0.75+0.2) = (0.75)(0)+(0.2)(1.7)

0.95 = 0.34

= 0.36 m/s

Now we can calculate the amplitude

A = 0.11  m

the period of the subsequent oscillations is T = 1.94 s

the equation for period is

T = 2π

T = 2π

T = 1.94 s