A 225kN test aircraft moving with velocity vo = xo = 25 km/h collides with a rigid barrier at t = 0. As a result of the behaviour of its energy absorbing capabilities, the response of the aircraft to the collision can be simulated by the damped spring- mass oscillator shown with k = 3MN/m and c = 840 kN.s/m. Assume that the mass is moving to the left with a velocity vo = xo = 25 km/h and the spring is unstretched at t = 0 determine the aircraft's deceleration: a) Immediately after it contacts the barrier; b) at t= 0.04s and; c) at t = 0.08s.

A 225kN test aircraft moving with velocity vo = xo = 25 km/h collides with a rigid barrier at t = 0. As a result of the behaviour of its energy absorbing capabilities, the response of the aircraft to the collision can be simulated by the damped spring- mass oscillator shown with k = 3MN/m and c = 840 kN.s/m. Assume that the mass is moving to the left with a velocity vo = xo = 25 km/h and the spring is unstretched at t = 0 determine the aircraft's deceleration: a) Immediately after it contacts the barrier; b) at t= 0.04s and; c) at t = 0.08s.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: A projectile of mass m = 10 kg traveling with the velocity v = 50 m/s strikes and becomes embedded…

Q: A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a…

Q: A long spring has a mass of 1 slug attached to it. The spring stretches 16/13 ft and comes to rest.…

Q: Two mass placed on top of each other have a mass of 20 g each and there is a coefficient of static…

A: At the position of amplitude the restoring spring force will be F=kAand therefore the acceleration…

Q: Problem 6. Fox Fork Fabrication Fox Factory Inc. is testing a new fork design. A step force of F=…

Q: 3. An undamped spring-mass system has a mass that weighs 48 lb and a spring constant 0.5 lb/in. The…

A: This question is related to the spring-mass system. The elastic vibration wherever there's no…

Q: A 2-kg mass is attached to a spring with stiffness 10 N/m. The damping constant for the system is…

A: The mass of block is The spring constant is .The damping constant is .The initial displacement is…

Q: 5. For a simple seismograph as shown in Figure Q5 below, the co-ordinate X₁ measures horizontal…

A: Here, The mass m=1 kg. The spring stiffness k=10 Nm-1. The coefficient of the damper, c=2Nsm-1.…

Q: 6. Consider the following model for a mechanical dynamic system consisting of a two linear springs…

Q: ha ZeroPotential Datum MA mg k

A: Given, μk=0.14 k=32.5 Nm hA1=0.6 m mA=4.6 kg mB=1.3 kg

Q: 3) Consider the simple pendulum-spring-mass system below, where mass m is added to the tip of the…

Q: The elastic foundation of a heavy machine in Figure Q19 consists of elastic springs connected in…

A: Given data:- the springs have stiffness coefficient (k) = 10000 N/m The machine is of mass (m) =1164…

Q: QI A projectile of mass m 10 kg traveling with the velocity v 50 m/s strikes and becomes embedded in…

A: Free vibration is the vibration of a system in response to initial excitation consist of initial…

Q: When testing the landing gear unit of a space vehicle drop tests are carried out. Figure 2.17 is a…

Q: The mass of the represented system is released under the initial conditions xo 0.1m and xo -5m/s…

A: Given : x0 = 0.1 m v0 = - 5 m/s To find: Response graph Time at x = -0.05 m

Q: The 8kg body Figure 4 is moved 0.2m to the right of the equilibrium position and released from rest…

Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

A 225kN test aircraft moving with velocity v = Xo = 25 km/h collides with a rigid
barrier at t = 0. As a result of the behaviour of its energy absorbing capabilities, the
response of the aircraft to the collision can be simulated by the damped spring- mass
oscillator shown with k = 3MN/m and c = 840 kN. s/m. Assume that the mass is
moving to the left with a velocity vo = xo = 25 km/h and the spring is unstretched at
t = 0 determine the aircraft's deceleration:
a) Immediately after it contacts the barrier;
b) att = 0.04s and;
c) at t= 0.08s.
Vo =
********
xo
******
Vo = xo
www
m
Figure Q5 - Aircraft Collision
F(t)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Equation of motion

VIEW

Step 3: Solution of equation of motion

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

I want the correct solution thank u
Q2B. In Figure Q2B, if h=700mm and d = 500mm and each spring has constant k = 600Nm, determine the equation of motion of the mass m. For what value of the mass m will the period of small oscillations be (i) 0.25 s (ii) Infinite Under damped Choral 04pr www Figure Q2B Xu) 20 (om wt +x)
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position x0 and initial velocity v0. Find the position function x(t) and determine whether the motion is over-damped, critically damped, or under-damped.
The car's corner mass is m₁ = 220 kg and the unsprung mass is m₂ = 16 kg. The suspension spring stiffness is k, = 13 kN/m and the tire stiffness is k = 150 kN/m. The car is traveling with speed V on a sinusoidal road surface with wavelength = 5 m and amplitude A, = 0.010 m. Neglect the suspension damping and use the complex frequency response method to find the steady-state responses of z₁ (t) and z₂ (t) for speeds from V = 5 m/s to V = 30 m/s in 5 m/s increments. Comment on the results. m₂ k₂ k₁ ZZZZ m₁ Z2 Z1 z, (t) = A, sin ot
PROBLEM1: Determine the equation of motion of the following systems: 1080 al*k www 0.51 ghiv Vin & Mass Less, Rigid L J Figure 2-Problem 1-2 a3*m
damping, c Sliding Crate with Bumper Stop A crate of mass m enters a lubricated slide at a loading dock with a velocity v, to the right and an initial position x(0) = x, in the diagram shown above. The sliding motion is lubricated, characterized by a linear damping coefficient C. At a distance x = L the crate contacts a bumper stop characterized by a spring constant k and a damping coefficient c. Numerical values for the system parameters are: C = 8 N-s/m k = 1000 N/m m = 50 kg X = 0 Vo = 5 m/s L= 20 m Ca is to be experimentally determined in completing this assignment Bumper: Assignment 1) Given these parameters, determine the governing dynamic equation for the crate position. 2) Convert the governing equation to state variable form. This requires two first-order equations: a. dv/dt f:(x,v) b. dx/dt = f.(x,v) where f, is a function of the states, x and v. where f, is a different function of the states, x and v. Make two sets of the above equations, one each depending on whether there…
!
An undamped free vibration system consisting of mass m = 5 kg and stiffnessa spring of 400 N/m, is given an initial displacement of 0.02 m and is kicked with an initial velocity of 0.1 m/s.Determine the equation of motion for the system.
A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 14 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ft
The mass of the system shown below is 10Kg. The mass is initially at rest when at time t=0, it is given an initial disturbance as shown. The viscous damping coefficient is 100NS/m and the spring stiffness, K is 100N/m. Which equation describes the movement of the mass. Disturbance Mass Spring Damper Select one: x(t) = (A, + A½t) e¯wnt a. %3D x(t) = A, e(-3+v?-1)wnt + A,e(-3-v?-1 )wnt x = (A3cos wat+ A4sin wat)e-wnt %3D C. Finish attempt.. evious page
Fast pls solve this question correctly in 5 min pls I will give u like for sure Anu
Hi, please answer this question. Thank you very much