You hav two heel trailer that you pul behind your ATV Tochildren with combined m

Question

You hav two heel trailer that you pul behind your ATV Tochildren with combined mess of 90 2 k trailer evera tree root in the trail,OSC!lates with period of 1. 74 s. Determine the following. hoo on board for ride through the oods and the sprigs(oefor each wheel each or press by 6 370m when you pul the a) force constant of the springs 032 (b) mass of the traler How is the period of esilation for an osoilating mass related to the force constant of the spring and the mass suspended by the spring? ko (c) frequency of the oscilation (d) tme it takes for the traller te bounce up and down 10 tmes

Explanation / Answer

(a) force constant of the springs
k = F/x
k = 90.2(9.81) / 0.0637
k = 13891 N/m

This is the combined spring constant for both springs. Each spring individually would have a spring constant of half that value or 6946 N/m

(b) mass of the trailer
T = 1.74 s
f = 1/T

= 0.575 Hz
f = /2
= 2f

= 3.611 rad/s
² = k/m
m = k / ²

   = 13891 / 3.611²

   = 1065.3 kg

so trailer mass is
m = 1065.3 - 90.2

    = 975 kg

(c) frequency of the oscillation
already found at 1/T
                   = 0.575 Hz

(d) time it takes for the trailer to bounce up and down 10 times

t = 10T = 17.4 s

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