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 DOWNUnder 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 1m below its equilibrium position, whereas y = -1 indicates it is 1mabove its equilibrium position.)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).Is the mass moving toward the ceiling or toward the floor at t = 7?Justify your answer with a calculation.At what time(s) in the first 2 seconds is the mass momentarilystationary?m

Answered: Image /qna-images/answer/44a9e930-6efc-4928-85f9-744ba39ad754.jpg

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.

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.