32 kg k- 12 kN/m Figure: Question 2 2. A 32-kg block is attached to a spring and can move without friction in a slot as shown. The block is in its equilibrium position when it is struck by a hammer, which imparts to the block an initial velocity of 250 mm/s. Determine a) the period and frequency of the resulting motion, b) the amplitude of the motion and the maximum acceleration of the block.

32 kg k- 12 kN/m Figure: Question 2 2. A 32-kg block is attached to a spring and can move without friction in a slot as shown. The block is in its equilibrium position when it is struck by a hammer, which imparts to the block an initial velocity of 250 mm/s. Determine a) the period and frequency of the resulting motion, b) the amplitude of the motion and the maximum acceleration of the block.

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 2.3-kg object is suspended using two linear springs (k1 = 45 N/m and k2 = 21 N/m), as shown below. Due to aerodynamic effects and other losses, you observe that the amplitude of the vibration is halved after 5 complete cycles. If the initial mass was displaced 270 millimetres below the equilibrium position (i.e. negative initial displacement) and then released from rest, determine the position of the mass after 11 seconds. Give your answer in millimetres rounded to one decimal place. Enter positive values if the mass is above the equilibrium position and negative values if it is below the equilibrium position. k k
Q2/ 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 has a dishpot 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.
The mass of a single degree damped vibrating system is 7.5 kg and makes 24 free oscillations in 14 seconds when disturbed from its equilibrium position. The amplitude of vibration reduces to 0.25 of its initial value after five oscillations. Determine : 1. stiffness of the spring, 2. logarithmic decrement, and 3. damping factor, i.e. the ratio of the system damping to critical damping.
A 25-kg mass is suspended from a spring with a constant of 2 N/mm, which is in turn suspended at the end of a steel cantilever beam with a thickness of 3mm, a width of 20 mm, and a length of 250 mm. Determine the natural frequency of the motion of the weight. + Hints: Please use stainless steel for the cantilever beam in this problem. Table 5 attached at the end of this assignment may come in handy. m The natural frequency w₂ can be found as wn = where k is the spring stiffness of the system and m is the mass.
Q1.Consider a 3-meter long pendulum placed on the moon and given an initial angulardisplacement of 0.4 rad and zero initial velocity. Note that gravity on the earth’s moon is ?? = ?/6, where g is the acceleration due to gravity on earth. (A) Write down the equation of motion for the pendulum (B) Calculate the amplitude of the angular displacement of the swinging pendulum
A 100-kg compressor rotor has a shaft stiffness of 1.4x 107 N/m. The compressor is designed to operate at a speed of 6000 rpm. The internal damping of the rotor shaft system is measured to be = 0.01. The rotor has an eccentric radius of 10mm.Determine: a) the displacement amplitude, X, at operating speed b) the critical speed ( in rpm) of the rotor system c) the whirl amplitude at critical speed.
mechanical principles Explain the natural frequency of vibration in a mass-spring system.
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.
QUESTION 2 A vibrating system can be modeled with a mass weighs 20 kg and supported on springs and dashpots. The total stiffness of the springs is 2000 N/m and the damping constant is 10 N/m/s. The system is initially at rest and a velocity of 10 m/s is imparted on the mass. Determine the displacement after 1 s.
A helical spring has a stiffness of of 25 kN/m. If a mass of 100 kg is attached to its free end, pulled down, and then released, (a) amount of deflection, in cm, (b) determine the periodic time of its motion. (c) If the maximum deflection was 50 mm, find the velocity and acceleration of the mass when it is 300 mm from the equilibrium position. Make an illustration.
A coil of spring stiffness 4 N/mm supports vertically a mass of 20 kg at the free end. The motion is resisted by the oil dashpot. It is found that the amplitude at the beginning of the fourth cycle is 0.8 times the amplitude of the previous vibration. Determine the damping force per unit velocity. Also find the ratio of the frequency of damped 'and undamped vibrations.
Problem 2 A railroad car of masse 20000 kg travelling at a velocity v=10 m/s is stopped at the end of the track by a spring-damper system. If the stiffness of the spring is k=40 N/mm and the damping constant c=20 Ns/mm, determine a) the maximum displacement of the car after engaging the springs and damper and b) the time taken to reach the maximum displacement.