A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Ae−λt sin ω2 − λ2t + ϕ , which is given in (23) of Section 3.8. (Round ϕ to two decimal places.) x(t) t + ϕ , which is given in (23) of Section 3.8. (Round ϕ to two decimal places.) x(t) = ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) s
A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Ae−λt sin ω2 − λ2t + ϕ , which is given in (23) of Section 3.8. (Round ϕ to two decimal places.) x(t) t + ϕ , which is given in (23) of Section 3.8. (Round ϕ to two decimal places.) x(t) = ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) s
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A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity.
(a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position.
(b) Express the equation of motion in the form
x(t) =
ft
(b) Express the equation of motion in the form
x(t) = Ae−λt sin
t + ϕ
,
which is given in (23) of Section 3.8. (Round ϕ to two decimal places.)
t + ϕ
,
which is given in (23) of Section 3.8. (Round ϕ to two decimal places.)| ω2 − λ2 |
x(t)
x(t) = ft
(c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)
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