Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
4. Periodic impulses. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is at equilibrium and is set into motion with a velocity of 6 inches per second. The mass is in a medium where friction is small, and we assume it is zero. Note that the acceleration due to gravity near the earth's surface where the experiment takes place can be taken as 32 ft/s². (a) Suppose that in addition to the conditions described above, a hammer strikes the mass every π/2 seconds starting at t = 0. A delta function with impulse of 1 pound-second models the force of each blow to the mass. Find the function x(t) for the displacement from equilibrium in feet of the mass at time t in seconds. Express x(t) as a piecewise defined function without the use of unit step or Heaviside functions and such that in each time window it is a different multiple of the same sinusoidal function. (b) Now assume the same spring-mass system is hit with a hammer strike more frequently, with a time delay of π/4 seconds between consecutive blows. Find x(t). Express x(t) following the guidelines in part (a). (c) Explain how the frequency of the blows affects the long term behavior of the system in parts (a) and (b).

4. Periodic impulses. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is at equilibrium and is set into motion with a velocity of 6 inches per second. The mass is in a medium where friction is small, and we assume it is zero. Note that the acceleration due to gravity near the earth's surface where the experiment takes place can be taken as 32 ft/s². (a) Suppose that in addition to the conditions described above, a hammer strikes the mass every π/2 seconds starting at t = 0. A delta function with impulse of 1 pound-second models the force of each blow to the mass. Find the function x(t) for the displacement from equilibrium in feet of the mass at time t in seconds. Express x(t) as a piecewise defined function without the use of unit step or Heaviside functions and such that in each time window it is a different multiple of the same sinusoidal function. (b) Now assume the same spring-mass system is hit with a hammer strike more frequently, with a time delay of π/4 seconds between consecutive blows. Find x(t). Express x(t) following the guidelines in part (a). (c) Explain how the frequency of the blows affects the long term behavior of the system in parts (a) and (b).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
See similar textbooks
icon
Related questions
Question

Please show all work!!

This most likely is made to be a probelm about mx''+bx'+kx=f(t)
m = mass
b = friction
k = spring constant
4. Periodic impulses. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is at equilibrium and is set into motion with a velocity of 6 inches per second. The mass is in a medium where friction is small, and we assume it is zero. Note that the acceleration due to gravity near the earth's surface where the experiment takes place can be taken as 32 ft/s². (a) Suppose that in addition to the conditions described above, a hammer strikes the mass every π/2 seconds starting at t = 0. A delta function with impulse of 1 pound-second models the force of each blow to the mass. Find the function x(t) for the displacement from equilibrium in feet of the mass at time t in seconds. Express x(t) as a piecewise defined function without the use of unit step or Heaviside functions and such that in each time window it is a different multiple of the same sinusoidal function. (b) Now assume the same spring-mass system is hit with a hammer strike more frequently, with a time delay of π/4 seconds between consecutive blows. Find x(t). Express x(t) following the guidelines in part (a). (c) Explain how the frequency of the blows affects the long term behavior of the system in parts (a) and (b).
Transcribed Image Text:4. Periodic impulses. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is at equilibrium and is set into motion with a velocity of 6 inches per second. The mass is in a medium where friction is small, and we assume it is zero. Note that the acceleration due to gravity near the earth's surface where the experiment takes place can be taken as 32 ft/s². (a) Suppose that in addition to the conditions described above, a hammer strikes the mass every π/2 seconds starting at t = 0. A delta function with impulse of 1 pound-second models the force of each blow to the mass. Find the function x(t) for the displacement from equilibrium in feet of the mass at time t in seconds. Express x(t) as a piecewise defined function without the use of unit step or Heaviside functions and such that in each time window it is a different multiple of the same sinusoidal function. (b) Now assume the same spring-mass system is hit with a hammer strike more frequently, with a time delay of π/4 seconds between consecutive blows. Find x(t). Express x(t) following the guidelines in part (a). (c) Explain how the frequency of the blows affects the long term behavior of the system in parts (a) and (b).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 12 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS