Question

A mass of five kilograms is mounted horizontally on a spring, with spring constant 1 Newton per meter, and friction coefficient 4 Newton-seconds per meter. The mass is in a magnetic field which exerts an additional force on the mass of constant strength 1 Newton. At time t = 0, the mass is at rest, at its equilibrium position. Write down the differential equation which describes the position of the mass, and compute its general solution.

Answer #1

When a mass of 4 kilograms is attached to a spring whose
constant is 64 N/m, it comes to rest in the equilibrium position.
Starting at t = 0, a force equal to f(t) = 80e−4t cos 4t is applied
to the system. Find the equation of motion in the absence of
damping.

When a mass of 3 kilograms is attached to a spring whose
constant is 48 N/m, it comes to rest in the equilibrium position.
Starting at t = 0, a force equal to
f(t) =
51e−2t cos
4t is applied to the system. Find the
equation of motion in the absence of damping.
x(t)= ?? m

A spring is mounted horizontally as shown to the right. A
crate,
which has a mass of 8.5 kg is pressed against the spring with
a
force of 350 N. As a result the spring is compressed a distance
of
82.0 cm. The mass is then released and is allowed to slide
along
the horizontal, frictionless surface.
a. What is the spring constant of this spring?
b. How much elastic potential energy will be stored in the
spring?
c. How...

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...

1.
A 0.12kg body is connected to a wall by a spring with a spring
constant of 570 N/m. The body experiences simple oscillatory motion
when pulled from its equilibrium rightward by 0.080m and then
released from rest. what is the displacement of the block after
0.20s.
2.
An object connected to a spring (with a spring constant of 29.8
N/m) is displaced 0.232 meter from equilibrium on a frictionless
horizontal tabletop; upon release, the object experiences simple
harmonic motion...

You drop an object with mass 3 kilograms from atop a building.
Suppose the air resistance constant is γ = 6 newton seconds per
meter. Let v(t) be the velocity of the object at time t. Write the
differential equation for v.

A 1-kilogram mass is attached to a spring whose constant is 16 N
/ m, and then the entire system is immersed in a liquid that
imparts a damping force equal to 10 times the instantaneous speed.
Determine the equations of motion if the mass is initially released
from a point 1 meter below the equilibrium position.
differential equations

. A block of mass 2.00 kg is attached to a horizontal spring
with a force constant of 500 N/m. The spring is stretched 5.00 cm
from its equilibrium position and released from rest. Use
conservation of mechanical energy to determine the speed of the
block as it returns to equilibrium
(a) if the surface is frictionless
(b) if the coefficient of kinetic friction between the block and
the surface is 0.350

A spring is compressed 1.5m by a a 4kg mass, which isn't
attached, and the spring has a force constant of 300N/m. Assume the
surface has no friction
How fast is the mass moving when it returns to equilibrium after
release?
How long does it take in seconds for the mass to return to the
equilibrium position after release?

A vertical ideal spring is mounted on the floor and has a spring
constant of 180 N/m. A 0.80-kg block is placed on the spring in two
different ways. (a) In one case, the block is placed on the spring
and not released until it rests stationary on the spring in its
equilibrium position. Determine the amount (magnitude only) by
which the spring is compressed. (b) In a second situation, the
block is released from rest immediately after being placed...

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