Question

A particular spring has a spring constant of 50 Newton/meters. Suppose a 1/2 kg mass is hung on the spring and is initially sent in motion with an upward velocity of 10 meters per second, 1/2 meter below the equilibrium position.

A) Write down the DE that models the motion of this spring.

B) Write down the initial conditions.

C) Find the equation of motion for the spring.

D) Suppose this spring mass system experiences a viscous damping term that is 6 times the instantaneous velocity. Write the DE that would model this system. DO NOT SOLVE THE DE.

E) Without solving the DE you wrote in part D, would this result in under, over, or critical damping? Show your work in determining this.

Answer #1

A spring-mass system has a spring constant of 3 Nm. A mass of 2
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viscous fluid that offers a resistance numerically equal to the
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an external force of 15cos(3t)−10sin(3t) N,determine the
steady-state response in the form Rcos(ωt−δ).
R=
ω=
δ=

A 1-kilogram mass is attached to a spring whose constant is 18
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x(t) = m
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A spring-mass system has a spring constant of 3 N/m. A mass of 2
kg is attached to the spring, and the motion takes place in a
viscous fluid that offers a resistance numerically equal to the
magnitude of the instantaneous velocity.
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released.
(a) Find a formula for the position of the mass as a function of
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(b) How much time does it take the mass to complete one
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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...

A 1-kilogram mass is attached to a spring whose constant is 16 N
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y(t)=
The damping factor is:
The quasiperiod is:
The quasifrequency is:

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