Question

Suppose that a car weighing 2000 pounds is supported by four shock absorbers Each shock absorber has a spring constant of 6250 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 25000 lbs/foot. 1. Assume no damping and determine the period of oscillation of the vertical motion of the car. Hint: g 32 f/sec2 T314 2. After 10 seconds the car body is 1 foot above its equilibrium position and at the high point in its cycle. What were the initial seconds. conditions? 2 0.4871 ft, and yt y(o,-0100X 0.487 ft. and y(0)- X ft/sec. 3. Now assume that oil is added to each the four shock absorbers so that, together, they produce an effective damping force of - 6.93 Ib-sec/ft times the vertical velocity of the car body. Find the displacement y(t) from equilibrium if y(0)-0 ft and y(0)--10 ft/sec. y(t)

Answer 1

Answer:

1).$T=0.314sec$

2).$y'(t)=21.24ft/s$

3).$y(t)=10*sin(16.66*t)$

Explanation:

1.

Time of the oscillation of the vertical motion of the car is

$T=2*\pi *\sqrt{\frac{m}{K}}$

$T=2*\pi *\sqrt{\frac{2000}{25000*32}} =2\pi *0.05$

$T=0.314sec$

2.

After 10 sec the car is at the high point of it's

$y(0)=1.0 ft$

$y(t)=-A*cos(wt)$

$y'(t)=A*w*sin(wt)$

$w=\frac{2\pi}{T}=16.66rad/s$

$y'(t)=62.05*sin(20.0181)$

$y'(t)=21.24ft/s$

3.

Coefficient r'

$r=\frac{6.93}{2*m}$

$r=0.0554$

$w'=\sqrt{w_o^2-r^2}=\sqrt{16.67^2-0.5544^2}$

$W'=16.66sec^{-1}$

$y(0)=0$

$y(t)=A*sin(w't)$

$y(t)=10*sin(16.66*t)$