A 64 lb object stretches a spring 4 ft in equilibrium. It is attached to a dashpot with damping constant c = 8 lb-sec/ft. The object is initially displaced 18 inches above equilibrium and given a downward velocity of 4 ft/sec. Find its displacement and time-varying amplitude for t > 0. 1.

A 64 lb object stretches a spring 4 ft in equilibrium. It is attached to a dashpot with damping constant c = 8 lb-sec/ft. The object is initially displaced 18 inches above equilibrium and given a downward velocity of 4 ft/sec. Find its displacement and time-varying amplitude for t > 0. 1.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 20P: A 200-g block is attached to a horizontal spring and executes simple harmonic motion with a period...

See similar textbooks

Related questions

Q: A device consists of an object with a weight of 20.0 N hanging vertically from a spring with a…

A: We know that a device consists of an object with the weight of W = 20 N and it hang vertically from…

Q: A 1.44-g spider oscillates on its web,which has a damping constant of 3.30 * 10-5 kg>s. How…

A: The amplitude of an oscillation subject to damping is given by this equation: x(t) = Ae^(-bt / (2m))…

Q: A 2.2 kg mass is attached to a horizontal spring with spring contant k= 4400 N/m. The spring is…

A: Given: The mass of the object is 2.2 kg. The spring constant is 4400 N/m. The spring is stretched 11…

Q: An object undergoes simple harmonic motion with a maximum velocity of vmax = 6.64 m/s. If it takes…

A: The equation for maximum velocity can be given by vmax=Aωvmax=A2πT

Q: A small bob is attached to a cord of length 1.2 m and is released from rest when 0A= 5°. Knowing…

Q: ki k1 ki W

A: Given: The amplitude of the oscillation is 0.045 m. The spring constant is 120 N/m. The period of…

Q: A 1.70 kg air-track glider is attached to a spring. The glider is pushed from rest and almost…

A: Given data:Mass of the air track glider, m = 1.70 kg.Instantaneous speed of the glider, Vmax = 0.960…

Q: Suppose that a car is 900 kg and has a suspension system that has a force constant k = 6.53X104 N/m.…

A: Given, Mass of car, m=900 kg, and force constant, k= 6.53×104 N/m, and amplitude, A=0.100 m.

Q: A suspension bridge oscillates with an effective force of 1 * 10^8 N/m. How much energy is needed…

A: It is given that

Q: An object attached to a spring vibrates with simple harmonic motion as described by the figure…

A: a) The Amplitude of the wave motion is define as the maximum displacement of the wave from it…

Q: A block-spring system consists of a spring with constant k = 455 N/m attached to a 2.75 kg block on…

Q: Suppose that a car is 900 kg and has a suspension system that has a force constant k = 6.53×104 N/m…

A: Given: mass, m = 900 kg spring constant, K = 6.53 x 104 N/m amplitude, A = 0.1 m

Q: A mass-spring system has a 7.1kg body attached to a spring with a force constant of 315N/m. The…

A: Given Mass is given as m=7.1 kg Force constant of the spring is k=315 N/m Maximum speed is vmax=0.4…

Q: The potential energy of an object attached to a spring is 2.60 J2.60 J at a location where the…

A: Given data: Potential energy (U) = 2.60 J Kinetic energy (K) = 1.20 J Amplitude (A) = 16.0 = 0.160…

Q: A simple harmonic oscillator of amplitude 5.00 m has a total energy of 8.00 J. a)Determine the…

Q: Which of the following is/are TRUE about an oscillation system under the critical damping condition?…

A: Here given the critical damping condition. We have to define which statements are true.

Q: A simple harmonic oscillator with m= 0.75 kg and total energy E=125 J has an amplitude of 1.5 m.…

Q: An object undergoes simple harmonic motion with a maximum velocity of vmax = 9.24 m/s. If it takes…

A: Let vmax be the maximum velocity of a simple harmonic motion, A be the amplitude of the motion, T be…

Q: A 3-kg mass is attached to a spring with stiffness 84 N/m. The damping constant for the system is…

A: Given: m = 3 kg k = 84 N/m b = 127 N-sec/m y(0) = 10 cm =0.1 m y'(0) = 3 m/s

Q: 4. A 1.5 kg block is attached to an ideal spring (k = 35 N/m). The end of the spring is then fixed…

A: mass of block m= 1.5 kgspring constant k= 35 N/mMaximum acceleration amax= 18.7 m/s2We know that…

Q: A block-spring system consists of a spring with constant k = 475 N/m attached to a 2.25 kg block on…

A: Write a given values of this question. k=475N/mm=2.25kg Pulled distance of block is 7.20cm.

Q: A 2.52 x 10-2-kg block is resting on a horizontal frictionless surface and is attached to a…

Q: A 1.20 kg air-track glider is attached to a spring. The glider is pushed from rest and almost…

A: The final speed of the glider (v),

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: Given: The amplitude is A=0.16 m. According to question. K=3U12kA2-x2=312kx2A2-x2=3x24x2=A2x=±A2

Q: A bullet weighing 25 g is immersed in a 600 g weight connected to a horizontal spring with a…

A: solution is given by

Q: A 2.30 kg frictionless block is attached to an ideal spring with force constant 317 N/m. Initially…

A: (1) Write the expression for the speed (v) of the block, and solve for the amplitude (A) of the…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: A 9.60-kg object oscillates at the end of a vertical spring that has a spring constant of 1.75 ✕ 104…

A: a) The angular frequency of damped oscillation can be represented as, Here, ω0, b, and m represent…

Q: 11. An 8 lb weight stretches a spring 2 inches. It is attached to a dashpot with damping constant…

A: The equation of motion is, Applying initial condition, the general solution is,

Q: A 35.0-g object connected to a spring with a force constant of 45.0 N/m oscillates with an amplitude…

A: Dear student, According to the guidelines I am allowed to answer only three…

Q: A 10.6 kg object oscillates at the end of a vertical spring that has a spring constant of 2.05×10^4…

Q: A 1.0 kg block sitting on a frictionless surface is connected to a massless spring of force constant…

A: Given: The mass of the object is 1 kg. The force constant is 30 N/m. The amplitude of the…

Q: An object attached to a spring oscillates on a frictionless horizontal track with an amplitude A =…

A: Given : A = 0.2 m v = 4 m/s

Q: In an electric shaver, the blade moves back and forth over a distance of 5 mm in simple harmonic…

Q: A simple harmonic oscillator consists of a 0.85 kg block attached to a spring. The block slides back…

A: Note : According to our guidelines , we are only allowed to answer 3 subparts per question . If you…

Q: A 4-kg mass is attached to a spring with stiffness 112 N/m. The damping constant for the system is…

Q: The potential energy of an object attached to a spring is 2.60 J at a location where the kinetic…

Q: A block-spring system has a maximum restoring force Fmax = 0.1 N. If the amplitude of the motion is…

Q: A blade of a helicopter oscillates with Simple Harmonic Motion such that its position in metres and…

A: I am doing first 3 sub-parts of this question due to honor code. Please upload the remaining part of…

Q: particle with mass 2.57 kg2.57 kg oscillates horizontally at the end of a horizontal spring. A…

Q: In the following exercises assume that there's no damping. C/G| An object stretches a spring 4…

Q: If the object-spring system is described by x = (0.335 m) cos (1.65t), find the following. (a) the…

Q: An automobile suspension system is critically damped, and its period of free oscillation with no…

A: The differential equation of a damped harmonic oscillator isx¨+gx˙+ωo2x=0where the angular frequency…

Q: An object with mass 2.2 kg k g is attached to a spring with spring stiffness constant 280 N/m N / m…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: A 20.5 kg object oscillates at the end of a vertical spring that has a spring constant of 3.04 x 10*…

A: Given that, the value of the object and spring constant and damping coefficient. Then We have to…

Q: The system shown below is subject to a sinusoidal base excitation with an amplitude of Y and…

A: Given:- N= 300 rpm M = 10 kg, c = 432N.s/m, K1 = 10 kN/m and K2 = 3K1. Find:- the ratio of…

Question

100%

A 64 lb object stretches a spring 4 ft in equilibrium. It is attached to a dashpot with damping
constant c = 8 lb-sec/ft. The object is initially displaced 18 inches above equilibrium and given a
downward velocity of 4 ft/sec. Find its displacement and time-varying amplitude for t > 0.
1.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.
Allow the motion in the preceding problem to take place in a resisting medium. After oscillating for 10 s, the maximum amplitude decreases to half the initial value. Calculate (a) the damping parameter β, (b) the frequency υ1 (compare with the undamped frequency υ0), and (c) the decrement of the motion.
The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?
Plot a velocity resonance curve for a driven, damped oscillator with Q = 6, and show that the full width of the curve between the points corresponding to is approximately equal to ω0/6.
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.
For a damped, driven oscillator, show that the average kinetic energy is the same at a frequency of a given number of octaves* above the kinetic energy resonance as at a frequency of the same number of octaves below resonance.
The mechanical energy of an undamped block-spring system is constant as kinetic energy transforms to elastic potential energy and vice versa. For comparison, explain what happens to the energy of a damped oscillator in terms of the mechanical, potential, and kinetic energies.
An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
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?
Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
If the amplitude of a damped oscillator decreases to 1/e of its initial value after n periods, show that the frequency of the oscillator must be approximately [1 − (8π2n2)−1] times the frequency of the corresponding undamped oscillator.