Instead of gently setting the load into the bed of the truck, the load is awkwar
ID: 2256687 • Letter: I
Question
Instead of gently setting the load into the bed of the truck, the load is awkwardly dropped into the bed from a height of 6 inches above the bed. How far does the rear of the truck sink down due to this dropped load?
The dropped load results in oscillations as the truck bed and load bounce up and down. Assume the shock absorbers are worn out and do not damp the oscillations. If the truck bed can be modeled as also weighing 1100 lbf, what is the frequency of these oscillations? What is the period of these oscillations? What is the amplitude of these oscillations?
Explanation / Answer
a) mg = kx ; k = 550 lbf/inch = 6600 lbf/foot
1100 = 45.83*x
x = 2 inches
b) Initially it is all PE , finally it is all spring energy
mg(h+x) = k*x*x/2 ; x is the distance sinked
1100*(0.5+x) = 6600*x*x*0.5
x = 7.3 inches
c) Angular frequency, omega = sqrt(k/m) = sqrt(550*32/1100) = 4 rad [m = 1100/g]
Linear ffrequency, f = w/2pi = 0.637 Hz
T = 1/f = 1.57 sec
Amplitude = 7.3 in