Question

A force of 400N stretches a string 2 meters. A mass of 50kg is attached to the end of the spring and stretches the spring to a length of 4 meters. The medium the spring passes through creates a damping force numerically equal to half the instantaneous velocity. If the spring is initially released from equilibrium with upward velocity of 10 m/s.

**a)** Find the equation of motion.

**b)** Find the time at which the mass attains its
extreme displacement from the equilibrium position.

Answer #1

A 4-foot spring measures 8 feet long after a mass weighing 8
pounds is attached to it. The medium through which the mass moves
offers a damping force numerically equal to
2
times the instantaneous velocity. Find the equation of motion if
the mass is initially released from the equilibrium position with a
downward velocity of 9 ft/s. (Use
g = 32 ft/s2
for the acceleration due to gravity.)
x(t) =
Find the time at which the mass attains its...

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from a point 1 foot above the equilibrium position with a downward
velocity of 12 ft/s. Determine the time at which the mass passes
through the equilibrium position. (Use g = 32 ft/s2 for the
acceleration due to gravity.)
s
Find the time after the mass...

A 4-foot spring measures 8 feet long after a mass weighing 8
pounds is attached to it. The medium through which the mass moves
offers a damping force numerically equal to
sqrt(2) times the instantaneous velocity. Find the equation of
motion if the mass is initially released from the equilibrium
position with a downward velocity of 9 ft/s. (Use
g = 32 ft/s2 for the acceleration
due to gravity.)
x(t) =
Find the time at which the mass attains its...

DIFFERENTIAL EQUATIONS
1. A force of 400 newtons stretches a spring 2 meters. A mass of
50 kilograms is attached to the end of the
spring and is initially released from the equilibrium position with
an upward velocity of 10 m/s. Find the equation of
motion.
2. A 4-foot spring measures 8 feet long after a mass weighing 8
pounds is attached to it. The medium through
which the mass moves offers a damping force numerically equal to
times the...

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3
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A mass weighing 19.6 N stretches a spring 9.8 cm. The
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(a) Find the equation of motion.
(b)Assume that the entire spring-mass system is submerged in a
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Determine the value of β so that the subsequent motion is
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A force of 64 pounds stretches a spring 4 feet. A mass of 4
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