A mass-spring-damper system, with constants m=6.5 kg, c=12N*s/m y k=6.5 N/m, It is released from rest from a distance x0=0.1 m. Determine: 1. The position and velocity of the mass at time t=2 seconds. 2. The times where the mass reaches its maximum and minimum values. 3. The variable amplitude of the oscillations.

A mass-spring-damper system, with constants m=6.5 kg, c=12N*s/m y k=6.5 N/m, It is released from rest from a distance x0=0.1 m. Determine: 1. The position and velocity of the mass at time t=2 seconds. 2. The times where the mass reaches its maximum and minimum values. 3. The variable amplitude of the oscillations.

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

The measurements on a mechanical vibrating system show that it has a mass of 8 kg and that the springs can be combined to give an equivalent spring of stiffness 5.4 N/mm. If the vibrating system have a dashpot attached which exerts a force of 40 N when the mass has a velocity of 1 m/s, find : 1. critical damping coefficient, 2. damping factor, 3. logarithmic decrement, and 4. ratio of two consecutive amplitudes.
A damped spring – mass system has a mass of 2 kg, a spring of stiffness 98 N/m and a dashpot with a viscous damping coefficient of 42 Ns/m. If the mass is disturbed by 70 mm and then released from rest, determine the displacement of the mass after 0·12 seconds
A damped single degree of freedom mass–spring system has a mass m = 3 kg,a spring stiffness k = 2700 N/m, and a damping coefficient c = 18 N·s/m. Themass is subjected to a harmonic force which has an amplitude F0 = 20 N anda frequency ωf = 15 rad/s. The initial conditions are x0 = 4 cm, and x˙0 = 0.Determine the displacement, velocity, and acceleration of the mass after timet = 0.5 s.
The following vibration system oscillates with a small angle. x = 0.6m, y = 1.8m, k = 18N/m. From the motor: static deflection = 0.2m, forcing frequency = 30 rad/s. If the starting angle from rest is 2 radians (counter-clockwise) and mass A is 10 kilograms, determine: 1. The natural frequency in radians per second. 2. The natural period in second 3. The amplitude of free vibration in meters (reference: neutral position of the spring below), 4. The amplitude of steady-state vibration in meters (reference: neutral position of the spring below) 5. The magnification factor 6. The overall displacement in meters when t= 1 second (reference: neutral position of the spring below).
A spring has a spring constant of k=18N/m, hung with a weight of mass m=½ kg. If the load is in an equilibrium position, then it is pulled and released with a speed of 3 m/s, then determine the equation of motion of the object if it does not experience friction or damping.
In the system shown,m= 2 kg, k= 1000 N/m, theta= 30 degrees and the friction coefficient between the block and the surface is u. (a) If the block is displaced from equilibrium and released, the decrease in amplitude per cycle is 2 mm. Determine the coefficient of friction u. (b) If the initial displacement is 5 cm from equilibrium, determine the time and position when the block comes to rest.
A spring-mass-damper system has a mass of 80 kg suspended from a spring having stiffness of 1000 N/m and a viscous damper with a damping coefficient of 80 N-s/m. If the mass is subjected to a periodic disturbing force of 50 N at an undamped natural frequency, determine (i) The undamped natural frequency. (ii) The damped natural frequency. (iii) The amplitude of forced vibration of mass. (iv) The phase difference.
A 2-kg block is supported by a spring with a constant of k= 128 N/m and a dashpot with a coefficient of viscous damping of c=0.6 N.s/m. The block is in equilibrium when it is struck from below by a hammer that imparts to the block an upward velocity of 0.4 m/s. Determine (a) the logarithmic decrement,(b) the maximum upward displacement of the block from equilibrium after two cycles.
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.
A mass of 0.75kg is attached to one end of a horizontal spring, of spring constant 400Nm-1. The other end of the spring is attached to a regid wall. The mass is pushed so that at time t=0 it is 4.0cm closer to the wall than the equilibrium position and is traveling towards the wall with a velocity of 0.50ms-1. a) determine the total energy of the oscillating system. b) obtain an expression for the displacement of the mass in the form x=Acid(wt+π)m, giving numerical values for A, w and phi
In the system below, the block has mass M = 2.0 kg, the spring has constant k = 500 N/m, and this spring-mass system is at rest. A projectile of mass m = 10g, with a speed of 800 m/s, collides with the block and becomes lodged inside. There is friction between the block and the floor on which it rests.a) What is the initial amplitude of the oscillation that the system acquires, right after the shock? Note: Assume the effect of friction on a single swing is negligible. b) Knowing that the amplitude is halved in 20 seconds, calculate the damping factor due to friction? c) How many oscillations, approximately, occurred in these 20 seconds?
Which of the following statements are valid for the rod below that is undergoing fixed axis rotation about pin O, where the spring constant is k = 115 N/m and the damping coefficient is c = 302 N.s/m? The slender rod has mass m = 17 kg and length L = 0.6 m. The differential equation governing the motion of the rod is given below. (In the statements below, wn denotes the natural frequency ωn, while wd denotes the damped frequency ωd.) a) Damped vibration, wn and wd not applicable b) Underdamped, wn = 2.60 rad/s, wd = 17.57 rad/s c) Overdamped, wn = 2.25 rad/s, wd not applicable d) Overdamped, wn = 2.60 rad/s, wd not applicable e) Underdamped, wn = 2.25 rad/s, wd = 26.55 rad/s