Question

A mass m = 2kg stretches a string by .5m. We also attach a damper of 24N as a speed of 3m/s. The initial position of the mass is 1m up and the initial velocity is 2m/s down. Setup the differential equation and find the particular solution for the displacement u(t).

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A force of 400N stretches a string 2 meters. A mass of 50kg is
attached to the end of the spring and stretches the spring to a
length of 4 meters. The medium the spring passes through creates a
damping force numerically equal to half the instantaneous velocity.
If the spring is initially released from equilibrium with upward
velocity of 10 m/s.
a) Find the equation of motion.
b) Find the time at which the mass attains its
extreme displacement...

A mass of 100 g stretches a spring 5 cm. If the mass is set in
motion from its equilibrium position with a downward velocity of 10
cm/s, and if there is no damping, determine the position u
of the mass at any time t. (Use g = 9.8
m/s2 for the acceleration due to gravity. Let
u(t), measured positive downward, denote the displacement in meters
of the mass from its equilibrium position at time t
seconds.)
u(t) =
When does...

with a complete solution
A body of mass 2 gr attached to a vertical spring stretches it
1000/4 cm to reach an equilibrium position. When the body moves in
the air it experiences a resistance opposite to its movement,
proportional to its speed, with a damping constant d = 10 gr/sec.
Approximate the acceleration of gravity by g = 1000 c m / s e c 2 .
b. Find a differential equation of the form y ′′ = F...

There is an object that weighs 8 pounds that stretches a spring
6 inches.
The system is inside a medium that transmits a force of 2ft-lb
when the speed of the object is 8ft/s.
We pull down the object 4 in and set in motion with an upward
velocity of 2 ft/s.
Question: a) Setup the initial value problem that describes the
motion of the object
b) Solve the differential equation

A mass of 1 kg stretches a spring 9.8 m. The mass is acted on by
an external force of 4 cos(t) N. If the mass is set in motion from
its equilibrium position with a downward velocity of 2 m/s, find
the position of the mass at any time. Identify the transient (i.e.,
complementary) and steady state (i.e., particular) solutions. Does
the motion exhibit resonance or a beat?

An
object of mass 2kg is free falling being given an initial velocity
of -10 m/s. its initial vertical position is 20 m.
a.) sketch v(t), y(t), and a(t) graphs for the motion.
b.) Find the time when the object reaches the ground.
c.) Find the velocity of the object at the impact
d.) Suppose that simultaneously another object is projected
straight up with an initial velocity of 10 m/s. prove if the other
project will pass the first.

3. A mass of 5 kg stretches a spring 10 cm. The mass is acted on
by an external force of 10 sin(t/2) N (newtons) and moves in a
medium that imparts a viscous force of 2 N when the speed of the
mass is 4 cm/s. If the mass is set in motion from its equilibrium
position with an initial velocity of 3 cm/s, formulate the initial
value problem describing the motion of the mass. Then (a) Find the...

A spring of negligible mass stretches 3.00 cm from its relaxed
length when a force of 7.30 N is applied. A 0.520-kg particle rests
on a frictionless horizontal surface and is attached to the free
end of the spring. The particle is displaced from the origin to
x = 5.00 cm and released from rest at t = 0.
(Assume that the direction of the initial displacement is positive.
Use the exact values you enter to make later calculations.)
(f)...

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 3.30 kg object hangs, at rest, on a 1.40 m long string
attached to the ceiling. A 109 g object is fired with a speed of 16
m/s at the 3.30 kg object, and the two objects collide and stick
together in an inelastic collision. Write an equation for the
motion of the system after the collision. Assume air resistance is
negligible. (Assume the collision occurs at t =
0. Let θ be the angle between the initial position...

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