A weight of mass 2 kg is placed on a long vertical spring with spring constant k = 20. The damping force is 4 dy/dt Newtons. The weight is moved 2 meters above its equilibrium position and is started in motion with a velocity of 1 meter/sec. upward. Find the equation of motion for the weight. (There is no external force).

A weight of mass 2 kg is placed on a long vertical spring with spring constant k = 20. The damping force is 4 dy/dt Newtons. The weight is moved 2 meters above its equilibrium position and is started in motion with a velocity of 1 meter/sec. upward. Find the equation of motion for the weight. (There is no external force).

Name: Please explain well A weight of mass 2 kg is placed on a long vertical
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: Please explain well A weight of mass 2 kg is placed on a long verticalspring with spring constant k=20. The dampingforce is 4 dy/dt Newtons. The weight is moved 2meters above its equilibrium position and is startedin motion with a velocity of 1 meter

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter15: Oscillations

Section: Chapter Questions

Problem 19CQ: Do you think there is any harmonic motion in the physical world that is not damped harmonic motion?...

See similar textbooks

Similar questions

We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.
A pendulum with a period of 2.00000 s in one location (g=9.80m/s2) is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location?
If a pendulum-driven clock gains 5.00 s/day, what fractional change in pendulum length must be made for it to keep perfect time?
Do you think there is any harmonic motion in the physical world that is not damped harmonic motion? Try to make a list of five examples of undamped harmonic motion and damped harmonic motion. Which list was easier to make?
If a car has a suspension system with a force constant of 5.00104 N/m , how much energy must the car’s shocks remove to dampen an oscillation starting with a maximum displacement of 0.0750 m?
Show that, if a driven oscillator is only lightly damped and driven near resonance, the Q of the system is approximately Q2(TotalenergyEnergylossduringoneperiod)
Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = bv2 and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, E=12mv2+12kx2, and use Equation 12.28.
a weight of 10 gm is attached to its free end. the Ex. 6: A light spring is stretched by 2 cm when weight is further pulled down by 1 cm and released. Find its frequency and amplitude.
4.9.9 Question Help A 3-kg mass is attached to a spring with stiffness 84 N/m. The damping constant for the system is 12/7 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 3 m/sec, what is the maximum displacement from equilibrium that it will attain? The maximum displacement is meters. (Type an exact answer, using radicals as needed.)
A mass weighing 4 N is attached to a spring whose constant is 2 N/m, The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 m above the equilibrium position with a downward velocity of 8 m/s. Determine the time at which the mass passes through the equilibrium position, (Use g - 9.8 m/s? for the acceleration due to gravity.) 0.678 Find the time after the mass passes through the equifibrium position at which the mass attains its extreme displacement from the equilibrium position. 0.678 What is the position of the mass at this instant? 1.383
A 5-kg mass is attached to a spring with stiffness 15 N/m. The damping constant for the system is 10√3 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 3 m/sec, what is the maximum displacement from equilibrium that it will attain? The maximum displacement is meters. (Type an exact answer, using radicals as needed.)