Question

use Matlab

Overview: The objective of a racetrack impact barrier is to slow a vehicle to a stop with minimal deceleration. It is also critical that the barrier not totally collapse. The figure below shows that the maximum displacement of the barrier wall (before total collapse) is 'd' meters. Kb The motion of the vehicle from the instant it strikes the barrier to the instant it begins "bounce back" is modeled by the following differential equation: Mä(t) + bż(t) + Kz(t) = 0 (0) = 0, ż(0) = V. where z(t) is the displacement of the vehicle, M is the mass of the vehicle, and K and b are the equivalent spring constant and damping coefficient of the barrier wall, respectively. Note: The differential equation above is only valid for the forward motion of the vehicle. Once the vehicle begins to bounce back, the equation becomes invalid.

Answer 1

50 19.- Given data, Allording to the above given Question by the following Solution as, vehicle massim] = 760K9 K = 29000nim b: R600 NSIM 210): 20 2100=26= 35 mis (a) the response of the system is given by the equation 7416) = efwne ( 70 Coreet + 204S wndo Sinugt) , Wd · lwhere I wo: Leon W = 6.179 radsec i = b - amon = 2600 X760X 6.177 Ś = 0.277 hid wiwin den er Scanned with CamScanner = 6.177 V 1-0.279% = 5.935 rad sec . .........

HA194 line 19 177 17+420 lel 7,1 1 uning these Dala vajalle, En e can be expressed as $33-6.- . $13 ,3" (33- Cry fot} = 331 411). Ean @ "saved in mano ab wing alou, The velville verronse and docetelakon are shown in the plons helow) adt) m 002 14 14 0 0 cs Scanned with CamScanner 0.04 0 0.08 Time (3) 0.40 0.19 ->

Substituting the value inlly, the response of the system is 411)¢ 58978141!! sin 5.9354 > he above response is valid only for the fol word motion of the Vehicle upto the time the welocity becomes & END Dif(clon halina rentating Eqh9 and getting is equal to gero, we get -) 5.891 (55.935 717"(08 5.9351-1.71819"sin 5.935+]=0 2114 A tan 5.9357 = 8.4687 t=0217User the wehille response is shown in the figure below. lum Gandawit 0-02 0.04 CamScanner 0.06 0.0 time 02 Diluoto O .

Notiche relatamon (roodby) - Decoration (3) 0.03 0.04 . 0 7.08 2 ·12 !4 Onit ott 02 as Scanned with CamScanner