Question
In: Advanced Math
A mass of 2 kg is suspended from a spring with known spring constant of 10N/m...
A mass of 2 kg is suspended from a spring with known spring constant of 10N/m and allowed to come to rest. it is then set in motion by giving it an initial velocity of 150 cm/sec. Find an expression for the motion of the mass, assuming no air resistance.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
A mass m = 1 kg is suspended from a spring that is stretched 1 cm...
A mass m = 1 kg is suspended from a spring that is stretched 1
cm
under the influence of the weight of this mass. Now a periodic
force is applied
external of F (t) = 200 cos (vt) on the mass, which was initially
in
static balance. Disregarding all friction, get a relationship
for
position of the mass as a function of time, x (t). Also determine
the value of
ω which will cause resonance to occur
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)...
A block of mass m = 2.5 kg is attached to a spring with spring constant...
A block of mass m = 2.5 kg is attached to a spring with
spring constant k = 640 N/m. It is initially at rest on an
inclined plane that is at an angle of θ = 27° with respect
to the horizontal, and the coefficient of kinetic friction between
the block and the plane is μk = 0.11. In the
initial position, where the spring is compressed by a distance of
d = 0.19 m, the mass is at...
A mass suspended at the end of a light Spring and spring constant K is set...
A mass suspended at the end of a light Spring and
spring constant K is set into vertical motion use lagrange's
equation to find the equation of motion of the mass
1. A mass weighting 8 pounds is suspended from a spring whose spring constant is 9...
1. A mass weighting 8 pounds is suspended from a spring whose
spring constant is 9 lb/ft. There are no damping or
external forces. The mass is then released from an initial
position of 5 feet above the equilibrium position with an
initial downward velocity of 30 ft/sec. (Note: Use g = 32
ft/sec!)
a) Write down an initial value problem modeling this
situation.
b) Find the equation of motion.
c) What are the amplitude, period, and frequency of the...
A spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 Nm. 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. If the system is driven by
an external force of 9cos(3t)−6sin(3t) N,determine the steady-state
response in the form Rcos(ωt−δ).
A spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is...
A spring-mass system has a spring constant of 3 Nm. 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. If the system is driven by
an external force of 15cos(3t)−10sin(3t) N,determine the
steady-state response in the form Rcos(ωt−δ)
A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences...
A 0.5-kg mass is attached to a spring with spring constant 2.5
N/m. The spring experiences friction, which acts as a force
opposite and proportional to the velocity, with magnitude 2 N for
every m/s of velocity. The spring is stretched 1 meter and then
released.
(a) Find a formula for the position of the mass as a function of
time.
(b) How much time does it take the mass to complete one
oscillation (to pass the equilibrium point, bounce...
A block of mass 1.59 kg is connected to a spring of spring constant 148 N/m...
A block of mass 1.59 kg is connected to a spring of spring
constant 148 N/m which is then set into oscillation on a surface
with a small coefficient of kinetic friction. The mass is pulled
back 30.6 cm to the right and released. On the first right to left
oscillation, the mass reaches 29.38 cm to the left.
Part A
What is the coefficient of friction?
Part B
To what distance does the mass return on the slide back...
a. A 0.5 kg mass attached to a linear spring, with spring constant 5 N/m and...
a. A 0.5 kg mass attached to a linear spring, with spring
constant 5 N/m and damping constant 0.2 kg/s, is initially
displaced 10 cm from equilibrium. (a) What is the natural frequency
of oscillation? What is its period of oscillation? How long does it
take for the amplitude to decrease to 10% of its starting value?
How many oscillations have occurred in this time? What fraction of
the initial energy remains after this time?
b. Two traveling waves with...
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