Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

A mass weighing 4 pounds stretches a spring 4 inches. (a) Formulate an initial-value problem that corresponds to the motion of this un-damped mass-spring system

A mass weighing 4 pounds stretches a spring 4 inches.

(a) Formulate an initial-value problem that corresponds to the motion of this un-damped mass-spring system if the mass is extended 7 foot from Its rest position and released (with no initial velocity).

(b) Using the result of Exercise, find the solution of this initial-value problem.

Referred Exercise

Consider the equation cry

d 2 y/dt 2 + (k/m) y = 0

for the motion of a simple harmonic oscillator

(a) Consider the function y(t) = cos βt. Under what conditions on β is y(t) a solution?

(b) What initial condition (t = 0) in the yv-plane corresponds to this solution?

(c) In terms of k and m, what is the period of this solution?

(d) Sketch the solution curve (in the yv-plane) associated to this solution.

[Hint. Consider the quantity y 2 + (v/β)2.]

Step by Step Solution

3.39 Rating (155 Votes )

There are 3 Steps involved in it

Step: 1

a Consider a mass weighing 4 pounds stretches a sprang 4 inches and let the mass is extended 1 foot ... blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

A First Course in Differential Equations with Modeling Applications

Authors: Dennis G. Zill

10th edition

978-1111827052

More Books

Students also viewed these Physics questions