A ball of mass 4 kg is placed at the lower end of a vertical spring, whose constant of restitution is 9 N/where the damping force is negligible, At the instant of t=0 the ball is 0.2 m below the equilibrium position, where a downward velocity of 1m/s is impressed on it. From instant , the external force g(t) = 18sen ()t in newtons is activated and intervenes in the System A- Set up a differential equation and the conditions that describe the position of the ball at time t in seconds B- Find the position function for the ball at any time t in seconds C- Determine the speed of the ball when t=1 s and the position at 5 seconds

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 18P
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A ball of mass 4 kg is placed at the lower end of a vertical spring, whose constant of restitution
is 9 N/where the damping force is negligible, At the instant of t=0 the ball is 0.2 m below the
equilibrium position, where a downward velocity of 1m/s is impressed on it. From instant , the
external force g(t) = 18sen )t in newtons is activated and intervenes in the System
A- Set up a differential equation and the conditions that describe the position of the ball at
time t in seconds
B- Find the position function for the ball at any time t in seconds
C- Determine the speed of the ball when t=1 s and the position at 5 seconds
Transcribed Image Text:A ball of mass 4 kg is placed at the lower end of a vertical spring, whose constant of restitution is 9 N/where the damping force is negligible, At the instant of t=0 the ball is 0.2 m below the equilibrium position, where a downward velocity of 1m/s is impressed on it. From instant , the external force g(t) = 18sen )t in newtons is activated and intervenes in the System A- Set up a differential equation and the conditions that describe the position of the ball at time t in seconds B- Find the position function for the ball at any time t in seconds C- Determine the speed of the ball when t=1 s and the position at 5 seconds
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