Question
In: Math
Suppose that the mass in a mass-spring-dashpot system with m = 10, the damping constant c...
Suppose that the mass in a mass-spring-dashpot system with m = 10, the damping constant c = 9, and the spring constant k = 2 is set in motion with x(0) = -1/2 and x'(0) = -1/4.
(a) Find the position function x(t).
(b) Determine whether the mass passes through its equilibrium position. Sketch the graph of x(t).
Solutions
milcah answered 2 years agoRelated Solutions
A spring with a mass of 1 kg has damping constant 10 kg/s and a spring...
A spring with a mass of 1 kg has damping constant 10 kg/s and a
spring constant 41 kg/s2 . If the spring begins at equilibrium
position and is given a velocity of 2 m/s, find the position of the
mass at any time t. Is this overdamping, critical damping or
underdamping?
A spring with a mass of 1 kg has damping constant 10 kg/s and a spring...
A spring with a mass of 1 kg has damping constant 10 kg/s and a
spring constant 41 kg/s2 . If the spring begins at equilibrium
position and is given a velocity of 2 m/s, find the position of the
mass at any time t. Is this overdamping, critical damping or
underdamping?
A particle of mass 1 is attached to a spring dashpot mechanism. The stiffness constant of...
A particle of mass 1 is attached to a spring dashpot mechanism.
The stiffness constant of the spring is 3 N/m and the drag force
exerted on the particle by the dashpot mechanism is 4 times its
velocity. At time t=0, the particle is stretched 1/4 m from its
equilibrium position. At time t=3 seconds, an impulsive force of
very short duration is applied to the system. This force imparts an
impulse of 2 N*s to the particle. Find the...
In a spring-mass-dashpot system, a force of 1 Newtons is required to stretch the spring for...
In a spring-mass-dashpot system, a force of 1 Newtons is
required to stretch the spring for .05 meters. A mass of 4 kg is
hung from the spring and also attached to a viscous damper that has
a damping constant 8 Newton-sec/m. The mass is suddenly set in
motion from its equilibrium location at t = 0 by an external force
of 8 cost Newtons with initial velocity 0 m/sec. Find the transient
solution and the steady state solution of...
Consider a mass-spring-dashpot system with mass 5kg, a spring which is stretched 3 meters by a...
Consider a mass-spring-dashpot system with mass 5kg, a spring
which is stretched 3 meters by a force of 10N, and a dashpot which
provides a 4N resistance for each m/s of velocity. The mass is also
acted on by a periodic force 5 cos(ωt) for some number ω.
• For what value of ω (if any) does practical resonance
occur?
• If the mass starts at rest, at equilibrium, find a formula for
x(t) (in terms of ω), the distance...
Consider a mass-spring-dashpot system with mass 5kg, a spring which is stretched 6 meters by a...
Consider a mass-spring-dashpot system with mass 5kg, a spring
which is stretched 6 meters by a force of 20N, and a dashpot which
provides 4N resistance for each m/s of velocity. The mass is also
acted on by a periodic force 5 cos(ωt) for some number ω. For what
value of ω (if any) does practical resonance occur? If the mass
starts at rest, at equilibrium, find a formula for x(t) in terms of
ω, the distance between the mass...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
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 resis- tance numerically equal to the
magnitude of the instanta- neous velocity. If the system is driven
by an external force of (12 cos 3t − 8 sin 3t) N, determine the
steady-state response.
(a) Find the gain function if the external force is f(t) =
cos(ωt).
(b)...
Consider a mass spring system. The spring has a constant k=30N/m and mass=3kg. The mass oscillates...
Consider a mass spring system. The spring has a constant k=30N/m
and mass=3kg. The mass oscillates w/amplitude of 10cm. a.)what is
the frequency of oscillation b.) what is the displacement at time
t=0 c.) when is the first time the mass is at maximum displacement?
(t=?) d.) what is the maximum acceleration felt by the mass? Where
in the motion does this occur? e.)what is the minimum acceleration
felt by the mass? Where in the motion does this occur? f.)What...
A 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that...
A 1-kg mass stretches a spring 20 cm. The system is attached to
a dashpot that imparts a damping force equal to 14 times the
instantaneous velocity of the mass. Find the equation of motion if
the mass is released from equilibrium with an upward velocity of 3
m/sec.
SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL
EQUATIONS)
SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL
EQUATIONS)
SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL
EQUATIONS)
SOLVE THIS USING MATLAB...
10. It has a mass m attached to a spring of elastic constant k and that...
10. It has a mass m attached to a spring of elastic constant k
and that suffers a damping b
proportional to the speed, being b = k / 2. If the initial
amplitude is A:
a) How long does it take until the amplitude is worth A /
2?
b) How long does it take until half of the initial energy has
dissipated?
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