Consider the spring-mass system depicted in Figure 10.8.4. At t = 0, the mass is pulled down a distance 1 unit from equilibrium and released from rest. After 3 seconds, the mass is dealt an instantaneous blow that imparts five units of impulse in the upward direction. The initial-value problem governing the motion of the mass is d'y + 4y = -58(t – 3), dy (0) = 0, dt y(0) = 1, where 5 8 (t – 3) describes the impulsive force that acts on the mass at t = 3, and the positive y-direction is downward. Determine the motion of the mass for all t > 0. %3D Positive y- direction Impulsive force acts after 3 s Figure 10.8.4: A spring-mass system in which friction is neglected and the only external force acting on the system is an impulsive force that imparts 5 units of impulse at 1 = 3. wwww

Consider the spring-mass system depicted in Figure 10.8.4. At t = 0, the mass is pulled down a distance 1 unit from equilibrium and released from rest. After 3 seconds, the mass is dealt an instantaneous blow that imparts five units of impulse in the upward direction. The initial-value problem governing the motion of the mass is d'y + 4y = -58(t – 3), dy (0) = 0, dt y(0) = 1, where 5 8 (t – 3) describes the impulsive force that acts on the mass at t = 3, and the positive y-direction is downward. Determine the motion of the mass for all t > 0. %3D Positive y- direction Impulsive force acts after 3 s Figure 10.8.4: A spring-mass system in which friction is neglected and the only external force acting on the system is an impulsive force that imparts 5 units of impulse at 1 = 3. wwww

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: the differential equation that describes the motion.

A: Spring constant k=8g/s2 and the mass stretched the spring by, l=245 cmThe damping coefficient…

Q: Consider the initial value problem modeling the motion of a spring-mass-dashpot system initially at…

A: The given IVP is

Q: Consider the system of differential equations: dx 2x – Y dt dy 5x – 2y dt Plot a well-labeled phase…

A: Consider a given system of ordinary differential equation: dxdt=2x-ydydt=5x-2y Plot a well-labelled…

Q: A mass of 1 slug stretches a spring 2ft and comes to rest at equilibrium. The system is attached to…

A: Given: 1 slug mass stretches a spring 2ft and comes to rest at equlibrium. Damping force equal to 8…

Q: (1) Assume the velocity of a particle at time t is given by the function v(t) = (3 + 4t, 5 – 7t,…

A: The velocity function of the particle at time t is v⇀(t) = (3 + 4t , 5 - 7t, 11t) which can be also…

Q: Given the acceleration of a particle is a(t) = . If the initial velocity is v(0) = and the initial…

Q: Here’s a differential equation: y '[t] = t + y[t] y[0] = -1 Use Euler’s faker with a jump size of 1…

A: Euler's method recursive formula: tn+1=tn+hyn+1=yn+hftn,yn,n=0,1,2,... Given: y'=t+yy(0)=-1 The aim…

Q: Given the acceleration of a particle is a(t) = . If the initial velocity is v(0) = and the initial…

A: Givena(t) = <3,9t,et>

Q: When a 5 kg mass is attached to a spring whose constant is 80 N/m, it comes to rest in the…

Q: A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

Q: The motion of a mass-spring system with damping is governed by y''(t) + by' (t) + 9y(t) = 0; y(0) =…

A: Given differential equationy″+by′+9y=0Let y=ert be the trial solution thenr2ert+brert+9ert=0Since…

Q: A 1-kilogram mass is attached to a spring whose constant is 14 N/m, and the entire system is then…

Q: A 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system is then…

Q: A mass weighing 4 pounds is attached to a spring with a spring constant of 2 lb/ft. The mass is…

Q: (Exercise 3.4.104) a) Find the general solution of x' = y,y' = -x. b) Sketch the phase portrait,…

A: Given: x'=y.y'=-x The given points are (1,0) and (3,0)

Q: Find the general solutioxn of y′ + y = e.

A: We have to find general solution of y'+y=e Solution: Given differential equation can be written as:…

Q: find v(t) given a(t) and the initial velocity a(t) = (t, 4), v(0) = (1/3 , −2)

A: To find the velocity function vt, we have to integrate the acceleration function at=t, 4. Use the…

Q: 2. (UC-3) A mass weighing 64 pounds stretches a spring 3.2 feet. The mass is initially released from…

A: Newton's 2nd law of motion for the system is, md2xdt2=-kx-βdxdt+ftd2xdt2+kmx+βmdxdt=ftm Now,…

Q: A mass-spring system is driven by a sinusoidal external force g(t) = 3 sin (t). The mass equals 1,…

Q: 2. Find the position of a particle if its acceleration is (t) = ti+ej + e ²² k and r(0) = -j+ k.…

Question

Consider the spring-mass system depicted in Figure 10.8.4. At t = 0, the mass is pulled
down a distance 1 unit from equilibrium and released from rest. After 3 seconds, the
mass is dealt an instantaneous blow that imparts five units of impulse in the upward
direction. The initial-value problem governing the motion of the mass is
d'y
+ 4y = -58(t – 3),
dy
(0) = 0,
dt
y(0) = 1,
where 5 8 (t – 3) describes the impulsive force that acts on the mass at t = 3, and the
positive y-direction is downward. Determine the motion of the mass for all t > 0.
%3D

Positive y-
direction
Impulsive force
acts after 3 s
Figure 10.8.4: A spring-mass
system in which friction is
neglected and the only external
force acting on the system is an
impulsive force that imparts 5
units of impulse at 1 = 3.
wwww

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

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the solution to the Initial Value Problem describing the horizontal motion of a mass attached to a spring, mx = -k(x - 1), x(0)=4, x(0) = 0, for m 1, k = 9, 14. Describe in words the motion of the mass.
solve a) dy dx y (0) = 1 b) y (0) y = 3 S using the initial condition
Pls answer question 1 part B
A mass weighing 16 lb stretches a spring 1/4 feet. The mass is attached to a viscous damper with a damping constant of 2 lb-s/ft and is set in motion from its equilibrium position with a downward velocity of 1/2 ft/s. a) Set up the initial value problem (differential equation). b) Solve the equation to find the position of the mass y at any time t. c) Determine when the mass first returns to its equilibrium position. Assume that the y-axis is directed downward.
Find v(t) given the acceleration a(t) = 2j and initial condition v(0) = i.
The motion of a mass-spring system with damping is governed by y"(t) + by' (t) + 64y(t) = 0; y(0) = 1, y' (0) = 0. Find the equation of motion and sketch its graph for b = 0, 10, 16, and 20.
3) Answer the question shown in the image
The motion of a mass-spring system with damping is governed by y''(t) + 8y'(t) + ky(t) = 0; y(0) = 2, and y'(0) = 0. Find the equation of motion and sketch its graph for k= 14, 16, and 18.