6. A 1kg mass is attached to a spring (with spring constant k = 4 N/m), andthe spring itself is attached to the ceiling. If you pull the mass down to stretch thespring past its equilibrium position, when you release the mass and observe its(vertical) position, it's said to undergo simple harmonic motion.AT RESTMASS PULLED DOWNwwwwUnder certain initial conditions, the mass's vertical position (in metres) relative to itsequilibrium position at time t, y(t), can be modelled by the equationy(t) = cos(2t) – sin(2t),(Note that y measures how much the spring has been stretched, so y = 1 indicatesthe mass is Im below its equilibrium position, whereas y = -1 indicates it is 1mabove its equilibrium position.)(a) Find expressions for the mass's (vertical) velocity v(t) (relative to itsequilibrium position) and the mass's (vertical) acceleration a(t) (relative to itsequilibrium position).(b) Is the mass moving toward the ceiling or toward the floor at t= T?Justify your answer with a calculation.(c) At what time(s) in the first 2 seconds is the mass momentarilystationary?

Answered: Image /qna-images/answer/9d95c0bd-21ea-4796-8ade-1a1c4c050000.jpg

(a) Find expressions for the mass's (vertical) velocity v(t) (relative to its equilibrium position) and the mass's (vertical) acceleration a(t) (relative to its equilibrium position). (b) Is the mass moving toward the ceiling or toward the floor at t = T? Justify your answer with a calculation.

(a) Find expressions for the mass's (vertical) velocity v(t) (relative to its equilibrium position) and the mass's (vertical) acceleration a(t) (relative to its equilibrium position). (b) Is the mass moving toward the ceiling or toward the floor at t = T? Justify your answer with a calculation.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Question

6. A 1kg mass is attached to a spring (with spring constant k = 4 N/m), and
the spring itself is attached to the ceiling. If you pull the mass down to stretch the
spring past its equilibrium position, when you release the mass and observe its
(vertical) position, it's said to undergo simple harmonic motion.
AT REST
MASS PULLED DOWN
wwww
Under certain initial conditions, the mass's vertical position (in metres) relative to its
equilibrium position at time t, y(t), can be modelled by the equation
y(t) = cos(2t) – sin(2t),
(Note that y measures how much the spring has been stretched, so y = 1 indicates
the mass is Im below its equilibrium position, whereas y = -1 indicates it is 1m
above its equilibrium position.)
(a) Find expressions for the mass's (vertical) velocity v(t) (relative to its
equilibrium position) and the mass's (vertical) acceleration a(t) (relative to its
equilibrium position).
(b) Is the mass moving toward the ceiling or toward the floor at t= T?
Justify your answer with a calculation.
(c) At what time(s) in the first 2 seconds is the mass momentarily
stationary?

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