A force of 5 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.6 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) = Aet sin( x(t) ft /w² - 2² + 4), which is given in (23) of Section 3.8. (Round & to two decimal places.) (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) S Consider the following LRC-series circuit. L = 1 h, R = 100, C = 0.0004 f, E(t) = 30 V, q(0) = 0 C, i(0) = 4A Find the general solution for charge q(t) on the capacitor. q(t) = C Find the initial conditions. 9(0) = 9'(0) = C C/s Find the charge q(t) on the capacitor and the current i(t). q(t) = i(t) = C A Find the maximum charge on the capacitor. (Round your answer to four decimal places.) с

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A force of 5 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.6 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) = Aet sin(
x(t)
ft
/w² - 2² + 4), which is given in (23) of Section 3.8. (Round & to two decimal places.)
(c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)
S
Transcribed Image Text:A force of 5 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.6 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) = Aet sin( x(t) ft /w² - 2² + 4), which is given in (23) of Section 3.8. (Round & to two decimal places.) (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) S
Consider the following LRC-series circuit.
L = 1 h, R = 100, C = 0.0004 f, E(t) = 30 V, q(0) = 0 C, i(0) = 4A
Find the general solution for charge q(t) on the capacitor.
q(t) =
C
Find the initial conditions.
9(0) =
9'(0) =
C
C/s
Find the charge q(t) on the capacitor and the current i(t).
q(t) =
i(t) =
C
A
Find the maximum charge on the capacitor. (Round your answer to four decimal places.)
с
Transcribed Image Text:Consider the following LRC-series circuit. L = 1 h, R = 100, C = 0.0004 f, E(t) = 30 V, q(0) = 0 C, i(0) = 4A Find the general solution for charge q(t) on the capacitor. q(t) = C Find the initial conditions. 9(0) = 9'(0) = C C/s Find the charge q(t) on the capacitor and the current i(t). q(t) = i(t) = C A Find the maximum charge on the capacitor. (Round your answer to four decimal places.) с
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