A mass weighing 4 pounds is attached to a spring with a spring constant of 2 lb/ft. The massis initially released from a point 1 foot above the equilibrium position with a downward velocityof 8 ft/s. Assume that the medium offers a damping force that is numerically equal to theinstantaneous velocity.(a)Find the equation of motion.(b)Determine the time at which the mass passes through the equilibrium position.(c)Find the time at which the mass attains its extreme displacement from the equilibriumposition. What is the position of the mass at this instant?

Consider a mass weighing 4 pounds attached to a spring whose constant is 2 lb/ft and the medium…

Answered: A mass weighing 4 pounds is attached to…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The density of air changes with height. Under some conditions density p, depends on height z, and temperature T according to the following equation where Po and A are both constants. A meteorological balloon ascends (i.e., starts at z = 1 and gains height) over the course of several hours. Complete parts (a) and (b) below. Az P(z,T) = Po e ..... dz v) and that the temperature changes over time (i.e., that T is given by a function T(t)), derive, using the chain rule, an expression for the rate of change of air density, (a) Assuming that the balloon ascends at a speed v (i.e., dt as measured by the weather balloon. Choose the correct answer below. dp Az dT O A. dt T2 dt dp %3D dt Az dT dp С. dt %3D + T dt dp Az) dT O D. dt T2) dt (b) Assume that v = 1, Po = 1, and A = 1 and that when t= 0, T= 1. Are there any conditions under which the density, as measured by the balloon will not change in time? That is, find a differential equation that T must satisfy, if dp = 0, and solve this…
High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about 1.2 m/s², and (2) the typical maximum speed attainable is about 8.8 m/s. You board an elevator on a skyscraper's ground floor and are transported 190 m above the ground level in three steps: acceleration of magnitude 1.2 m/s² from rest to 8.8 m/s, followed by constant upward velocity of 8.8 m/s. then deceleration of magnitude 1.2 m/s² from 8.8 m/s to rest. T Part A Determine the elapsed time for each of these 3 stages. Express your answers using two significant figures separated by commas. tace, tconstant, tdec = Submit Part B AFN,acc AFN,constant FN FN Submit Request Answer 2 [5] ΑΣΦ Determine the change in the magnitude of the normal force, expressed as a % of your normal weight during each stage. Express your answers using two significant figures separated by commas. 2 AFN,dec FN Request Answer Part C Complete…
A mass weighing 16 pounds stretches a spring 8 feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a 1 damping force that is numerically equal to - the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration 2 due to gravity.) x(t) = ft
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