2.22. A projectile of mass m = 10 kg traveling with the velocity v ==.50 m/s strikes and becomes6.4 x 104 N/m inembedded in a massless board supported by a spring of stiffness kparallel with a dashpot with the coefficient of viscous damping c = 400 N s/m (Fig. 2.24).Determine the time required for the board to reach the maximum displacement and the valueof the maximum displacement.mkCx(t)FIGURE 2.24Projectile striking a board restrained by aspring and dashpotPARA? 2.22. A projectile of mass m = 10 kg traveling with the velocity v ==.50 m/s strikes and becomes6.4 x 104 N/m inembedded in a massless board supported by a spring of stiffness kparallel with a dashpot with the coefficient of viscous damping c = 400 N s/m (Fig. 2.24).Determine the time required for the board to reach the maximum displacement and the valueof the maximum displacement.mkCx(t)FIGURE 2.24Projectile striking a board restrained by aspring and dashpotPARA?

Given data: Mass of projectile, m = 10 kg Velocity of projectile, v = 50 m/s Stiffness of spring, k…

2.22. A projectile of mass m = 10 kg traveling with the velocity v = 50 m/s strikes and becomes embedded in a massless board supported by a spring of stiffness k 6.4 x 104 N/m in parallel with a dashpot with the coefficient of viscous damping c = 400 N s/m (Fig. 2.24). Determine the time required for the board to reach the maximum displacement and the value of the maximum displacement.

2.22. A projectile of mass m = 10 kg traveling with the velocity v = 50 m/s strikes and becomes embedded in a massless board supported by a spring of stiffness k 6.4 x 104 N/m in parallel with a dashpot with the coefficient of viscous damping c = 400 N s/m (Fig. 2.24). Determine the time required for the board to reach the maximum displacement and the value of the maximum displacement.

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 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
A railroad bumper is designed as a spring in parallel with a viscous damper. What is the bumper's damping coefficient such that the system has a damping ratio of 1.25 when the bumper is engaged by a 20,000-kg railroad car and has a stiffness of 2 x 10^3 N/m? In a moment the railroad car travels on a speed of 20 m/s when it engages the bumper. What is the maximum deflection of the bumper? Another empty railroad car has a mass of only 4500 kg. What are the natural frequency and a damping ratio of a system with the when engaged by an empty railroad car?
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?
A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 5 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.)
4.4. A spring-mass system is subjected to a harmonic force which has an amplitude 30N and frequency 20 rad/s. The system has mass m = 5 kg, and stiffness coefficient k= 2 x 10° N/m. The initial conditions are such that xo = 0, io = 2 m/s. Determine the displacement, velocity, and acceleration of the mass after 0.5, 1, 1.5 s.
4.3. In a single degree of freedom undamped spring-mass system, the mass m = 3 kg, and the stiffness coefficient k = 2 x 103 N/m. The system is subjected to a harmonic forcing function which has an amplitude 60 N and frequency 30 rad/s. The initial conditions are such that xn = 0.0m and io = 1 m/s. Determine the displacement, velocity, and acceleration of the mass after t = 1 s.
5 rad/s A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with an amplitude A = 0.16 m. At what position (x = ?) would the kinetic energy of the system be equal to three times its elastic potential energy (K = 3U)? %3D At x = +0.1 m O At x = 10.05 m At x = +0.025 m OAt x = +0.04 m At x = +0.08 m
A rail road bumper is designed as a spring in parallel with a viscous damper. What is the bumper's damping coefficient such that the system has a damping ratio of 1.25, when the bumper is engaged by a rail car of 20,000 kg mass. The stiffness of the spring is 200 kN/m. If the rail car engages the bumper, while traveling at a speed of 20m/s, what is the maximum deflection of the bumper? poooo m
A 25 kg mass is attached to a spring with spring constant 100 N/m. The mass is driven by an external force equal tof(t) = 5 cos(2t). The mass is initially released from rest from a point 1 m below the equilibrium position. (Use theconvention that displacements measured below the equilibrium position are positive.) Write the initial-value problem which describes the position of the mass.
4. A mass-spring system exhibits a period of 5 s and a measured mass of 20 kg. Calculate the spring stiffness k.
The spring-damper-mass system shown in Figure Q3(c) is at rest when strict bya hammer with an initial velocity of 0.4 m/s causing the mass to move upwards.Given that the mass m = 2 kg, spring constant k = 128 N/m and coefficient ofviscous damping c = 0.6 Ns/m.(i) Determine the damped frequency of the spring-damper-mass system.(ii) Base on the given conditions derived in Q3(c)(i) and parameters givenabove, describe how you would derive the equation of motion ofdamped-free vibration.
When testing the landing gear unit of a space vehicle drop tests are carried out. Figure 2.17 is a schematic model of the unit at the instant when it first touches the ground. At this instant the spring is fully extended and the velocity of the mass is () where h is the height from which the unit has been dropped. Obtain the equation representing the displacement of the mass at time t>0 when M=50kg B = 180 Nsm^-1 and k = 474.5 N m^-1, and investigate the effects of different dropping height h. (g is the acceleration due to gravity and my be taken as 9.8 ms^-2.) and the velocity of the mass is √(2gh), where h is the height from which the unit has been dropped. Obtain the equation representing the displacement of the mass at time t> 0 when M = 50 kg, B = 180 N sm and K = 474.5 Nm, and investigate the effects of different dropping heights h. (g is the acceleration due to gravity, and may be taken as 9.8 m s².) eeeee M 19 x(t)