Question

Using the Newton’s second law model for a vibrating mass-spring system with damping and no forcing, 〖my〗^''+by^'+ky=0, find the equation of motion if m=10 kg, b=40 kg/sec, k=240 kg/sec2, y(0)=1.0, and y^' (0)=0.0 m/sec.

Answer #1

Using the Newton’s second law model for a vibrating spring with
damping and no forcing, 〖my〗^''+by^'+ky=0, find the equation of
motion if m=10 kg, b=60 kg/sec, k=50 kg/sec2, y(0)=0.3, and y^'
(0)=-0.1 m/sec. What is the position of the mass after 1 second?
Show all work.

Using the Newton’s second law model for a vibrating spring with
damping and no forcing,
my"+by'+ky=0, find the equation of motion if m=10kg, b=60kg/sec,
k=50kg/sec^2, y(0)=0.3, and y'(0)=-0.1m/sec. What is the mass after
1 second? Show all work.

A 1/2 kg mass is attached to a spring with 20 N/m. The
damping constant for the system is 6 N-sec/m. If the mass is moved
12/5 m to the left of equilibrium and given an initial rightward
velocity of 62/5 m/sec, determine the equation of motion of the
mass and give its damping factor, quasiperiod, and
quasifrequency.
What is the equation of motion?
y(t)=
The damping factor is:
The quasiperiod is:
The quasifrequency is:

A 1/4-kg mass is attached to a spring with stiffness 52 N/m.
The damping constant for the system is 6 N-sec/m. If the mass is
moved 3/4 m to the left of equilibrium and given an initial
rightward velocity of 1 m/sec, determine the
equation of motion of the mass y(t) =
and give
its damping factor,
quasiperiod, and
quasifrequency.

consider a spring mass system with a damping force but no
external force that has the following equation of motion. Find the
damping constant c that gives the critical damping
x'+cx'+9x=0 x(0)=2 x'(0)=0

Consider a system with a vibrating base. The spring constant is
given as K = 10.kN/m and the mass is also given as M = 200.Kg. If
the amplitude of the base is 0.5mm, then what should the damping
constant c be for the amplitude of the transmitted force to be
equal to 2500.N at resonance.

A spring-mass-dashpot system has a mass of 1 kg and its damping
constant is 0.2 N−Sec m . This mass can stretch the spring (without
the dashpot) 9.8 cm. If the mass is pushed downward from its
equilibrium position with a velocity of 1 m/sec, when will it
attain its maximum displacement below its equilibrium?

An oscillator of mass 2 Kg has a damping constant of 12 kg/sec
and a spring constant of 10N/m. What is its complementary position
solution? If it is subject to a forcing function of F(t)= 2*sin(2t)
what is the equation for the position with respect to time?
Equation 2(x2) + 12(x1) + 10(x) = 2*sin(2t); x2 is the 2nd
derivative of x; x1 is the 1st derivative of x.

1. Consider a damped mass-spring system with
m=6
and
k=10
being subjected to harmonic forcing. Find the value of the
damping parameter
b
such that the driving frequency that maximizes the amplitude of
the response is exactly half of the natural (undamped) frequency of
the system.

a mass-spring system is driven by a constant external 16. the
mall equals 1, the spring constant equals 2, and the damping
coefficient equals 2. so the motion is given by y"+2y'+2y=16
if the mass is initially located at y(0)=1, with a velocity
y'(0)=0 find the equation of its motion

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