For a damped simple harmonic oscillator, the block has a mass of 1.1 kg and the spring constant is 13 N/m. The damping force is given by-b(dx/dt), where b = 220 g/s. The block is pulled down 14.7 cm and released. (a) Calculate the time required for the amplitude of the resulting oscillations to fall to 1/3 of its initial value. (b) How many oscillations are made by the block in this time?

For a damped simple harmonic oscillator, the block has a mass of 1.1 kg and the spring constant is 13 N/m. The damping force is given by-b(dx/dt), where b = 220 g/s. The block is pulled down 14.7 cm and released. (a) Calculate the time required for the amplitude of the resulting oscillations to fall to 1/3 of its initial value. (b) How many oscillations are made by the block in this time?

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 1-kg block attached to an Ideal massless spring and fixed on the other end on a horizontal frictionless surface. This block oscillates with an amplitude of 0.3 m and reaches a maximum speed of 5 m/s. What is the spring constant in N/m?
A spring is attached to the ceiling and pulled 14 cm down from equilibrium and released. The damping continuous constant for the spring is determined to be 0.4 and the spring oscillates 15 times each second. Find an equation for the displacement, D, of the spring from equilibrium in terms of seconds, t. D(t)=
A rotating machine of 400 kg is similar to the system shown below. It operates at 3600 rpm (note: 1 rpm = 2π/60 rad/s). The machine is unbalanced such that its effect is equivalent to a 4 kg mass located 20 cm from the axis of rotation. An isolator with a spring stiffness of 8x106 N/m and a damping constant of 2x104 Ns/m is placed between the machine and the foundation. Determine the steady state response of the system. Find the force transmitted to the foundation and transmissibility of the isolator. Find the damping ratio of the system ζ . Find the transmissibility of the system, Tf. Find the frequency ratio of the system, β. Find the amplitude of the harmonic excitation force of the system, Fo in Newton (N). Find the displacement amplitude of the steady state response of the system, X in millimeters (mm). Find the damped frequency of the system, ωd in rad/s. Find the force transmitted to the foundation, FT in Newton (N). Find the frequency of the harmonic…
1. Mass suspended simple harmonic motion (measured from equilibrium position), displacement, velocity, and acceleration are x = 75mm, 450 mm/s, a = -442.5 mm/s^2. Period of Vibration and the amplitude of motion. 2. A uniform of rod of mass m = 3kg is supported by a pin at its midpoint c and is attached to a spring constant k = 120 N/m. If end A is given a small displacement, and released, determine the T of it resulting motion A k = 120 N/m = 3kg m = B
Given an oscillator of mass 2.0kg and spring constant of 180N/m, what is the period without damping? Use numerical methods to model this oscillator with an additional friction force equal to where c is a positive damping constant. Using c=5.0, what is the new period of oscillation. What about for c=10? Assume initial position is 0.2m and initial velocity is zero. Please find the period using the position versus time plot and use the first full cycle of the motion.
QI: A portion of an automobile suspension system consists of an elastic spring and a viscous damper, as shown. If the natural frequency is 10 rad/sec, a) Determine the damping ratio so that any oscillations that occur will decay from 11-0.5 m to x2-D 0.025 m. b) If the system is displaced 0.2 m from its equilibrium position, and released from rest, determine the position of the mass after it has ascillated through 3 cycles.
A rotating machine of 400 kg is similar to the system shown below. It operates at 3600 rpm (note: 1 rpm = 2π/60 rad/s). The machine is unbalanced such that its effect is equivalent to a 4 kg mass located 20 cm from the axis of rotation. An isolator with a spring stiffness of 8x106 N/m and a damping constant of 2x104 Ns/m is placed between the machine and the foundation. Determine the steady state response of the system. Find the force transmitted to the foundation and transmissibility of the isolator. Find the damping ratio of the system ζ . Find the transmissibility of the system, Tf. Find the frequency ratio of the system, β. Find the amplitude of the harmonic excitation force of the system, Fo in Newton (N). Find the displacement amplitude of the steady state response of the system, X in millimeters (mm). Find the damped frequency of the system, ωd in rad/s. Find the force transmitted to the foundation, FT in Newton (N). Find the frequency of the harmonic…
(b) Consider a damped harmonic oscillator for which m is 0.05 kg and k is 5.0 N/m. State and sketch the nature of the nature of the oscillatory motion when the damping constant b is (i) 0.1 N – s/m, (ii) 1.0 N – s/m and (iii) 5 N – s/m.
A mass is suspended from a spring and is pulled down 3 cm from equilibrium and released. It completes a period in 2 seconds. Ignoring damping factors, find the function for the displacement from equilibrium h(t) in centimeters t seconds after the mass is released.
a mass-spring-damper system has a mass of 100 kg. In 60 s, its free response apmplitude decays such that the amplitude of the 30th cycle is 20% of the amplitude of the 1st cycle. Estimate the damping constant c and the spring constant k.
For a system with mass 10 kg, spring constant 100 N/m, damping ratio 1 kg/s, rotating unbalance of 0.1 kg, radius 100 cm, and driving frequency 50 Hz, what is the amplitude of the particular solution? What is the phase lag of the particular solution?
Q.4 A damped single degree of freedom mass-spring system is excited at resonance by a harmonic forcing function which has an amplitude of 40 N. The system has mass m of 3 kg, a stiffness coefficient k of 2700 N/m, and a damping coefficient c of 20 N·s/m. If the initial conditions are such that xo = 5 cm, and xo = 0, determine the displacement, velocity, and acceleration of the mass after t = 0.2 s.