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

Similar questions

A mass weighing 16 pounds stretches a spring 4 feet. The medium offers a damping force that is numerically equal to 3 times the instantaneous velocity. The mass is initially released from rest from a point 3 feet above the equilibrium position. (a) Find the equation of motion. (b) Will the mass pass through the equilibrium position? if yes, find the time when it occurs. Justify your answer.
A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 8 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to - the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 25 cos(3t). (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = ft
* F2 # 3 E Problem 4. EOM Derivation Derive the equation of motion for the following system: We want to measure the spin rate w of the rotating shaft of a turbine. To do it we push a small mass m against the end of the shaft. The shaft makes friction contact with the drag cup mounted on the mass. The frictional torque is b (w). Assume that the rotational spring torque is ke and that the moment of inertia of mass m is J. J Rotating Shaft F3 @ $ 4 R b J, m Drag Cup F4 Q Search % 5 F5 T 0 Wall * A 6 F6 Y 2 * F7 & 7 PrtScn U F8 4 8 Home 6. F9 9 End F10 Po 0
When a tree branch bends, it can be assumed that acts as a spring, i.e there is a restoring force −kx in response to a vertical deflection x. Internal friction of wood provides the dominant cushioning and is independent of the hanging mass, that is, F = −bẋ with b constant. We observe that a monkey of mass m1 hangs from the branch. East monkey oscillates many times, up and down before damping off appreciably, and coming to equilibrium. Then a second monkey of mass m2 hangs from the first monkey, and we observe that the monkeys together also oscillate several times before the branch reaches equilibrium. So the new equilibrium position of the branch is three times larger than with a single monkey. Besides, the energy loss per cycle for a monkey is half that of the loss with two monkeys. Based on these observations, determine the mass of each monkey (m1 and m2) in terms of a elastic constant k of the branch and a friction coefficient of the wood b. (Note: k and b are data)
Damped Oscillatory Motion The setup consists of a mass m and a mass ", connected by a massless string of length { via a massless pulley. There is no friction between the string and the pulley. Mass m/2 is connected to a spring (spring constant k) and to a damper, damping constant b. Write down the equation of motion for the mass m. Use the coordinate x, with x = 0 being the equilibrium position of the system. Question т m/2] k b
Consider the system shown in the figure in which a harmonic force acts on the mass m. Derive the condition under which the steady-state displacement of mass m will be zero. Disc, mass M Rolls without slipping Pulley Cord Fo sin ot m
Problem (6) A 25 kg mass is resting on a spring of 4900 N/m and dashpot of 147 N-se/m in parallel. If a velocity of 0.10 m/sec is applied to the mass at the rest position, what will be its displacement from the equilibrium position at the end of first second?
4. A mass-spring system exhibits a period of 5 s and a measured mass of 20 kg. Calculate the spring stiffness k.
8. A spring of 21 cm length reaches 30.8 cm after hanging a mass of 1/4 kilogram on it. The medium through which the mass moves provides a damping force equal to three times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward velocity of 2 m/s. Calculate the time at which the mass reaches its extreme displacement, and what is the position of the mass at that moment? (Use g = 9.8 m/s²) Sol.
The system shown below consists of two blocks moving to the right with a velocity of 7 m/s, where the system is dictated to move in a track as shown. The mas of each block is m = 4kg, and the stiffness of each spring is k = 2500N/m, and modal damping ratio for each damper equal to 0.05, determine: 1. The equation of motion in matrix form. 2. The equation of motion of each block in the modal coordinates (i.e. ri(t),r2(t)). 3. Suggest a solution to make better isolation of the two blocks
A 0.1 kg object oscillates as a simple harmonic motion along the x-axis with a frequency f = 3.185 Hz. At a position x1, the object has a kinetic energy of 0.7 J and a potential energy 0.3 J. What tge amplitude of oscillation
A point mass is executing simple harmonic motion with an amplitude of 10 mm and frequency of 4 Hz. The maximum acceleration (m/s2 ) of the mass is