Question

DIFFERENTIAL EQUATIONS: An object stretches a spring 5 cm in equilibrium. It is initially displaced 10 cm above equilibrium and given an upward velocity of .25 m/s. Find and graph its displacement for t > 0. Find the frequency, period, amplitude, and phase angle of the motion.

Answer #1

A mass of 3 kg stretches a spring 61.25 cm. Supposing that there
is no damping and that the mass is set in motion from 0.5 m above
its equilibrium position with a downward velocity of 2 m/s,
determine the position of the mass at any time. Find the amplitude,
the frequency, the period and the phase shift of the motion.

A 5 kg object is attached to a spring and stretches it 10cm on
its own. There is no damping in the system, but an external force
is present, described by the function F(t) = 8 cos ωt. The object
is initially displaced 25 cm downward from equilibrium with no
initial velocity and the system experiences resonance. Find the
displacement of the object at any time t.

A mass weighing 16 pounds stretches a spring 1 feet. It is
initially released from a point 1 foot above the equilibrium
position with an upward velocity of 6 ft/s. Find the equation of
motion. Determine the amplitude, period, and frequency of motion.
(Use g = 32 ft/s2 for the acceleration due to gravity.)

A spring of negligible mass stretches 3.00 cm from its relaxed
length when a force of 7.10 N is applied. A 0.440-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.)
(a)...

If a 1 kg object on a horizontal, frictionless surface is
attached to a spring, displaced, and then released, it will
oscillate. If it is displaced 0.120 m from its equilibrium position
and released with zero initial speed. After 0.8 s its displacement
is found to be 0.120 m on the opposite side, and it has passed the
equilibrium position once during this interval. Find the amplitude,
the period, the frequency, the angular frequency and the spring
constant.

A
mass weighing 3 lb stretches a spring 3 in. If the mass is pushed
upward, contracting the spring a distance of 1 in, and then set in
motion with a downward velocity of 2 ft/s, and if there is no
damping, find the position u of the mass at any time t. Determine
the frequency, period, amplitude, and phase of the motion

An object of mass m = 0.25 kg has a horizontal spring attached
to its left side, and slides along a frictionless surface. The
spring constant is κ = 0.4 N m . At t = 0 s, the object is
displaced 0.1m to the right of its equilibrium position. Its
initial velocity is 0.4 m s , toward the right.
a) Calculate the period T of the motion. b) Calculate the
angular frequency ω. c) Calculate the frequency ν....

Applications of higher order differential equations
A spring has one of its ends fixed, and a force of 15 N
stretches it 20cm. A mass of 4 Kg is attached to the end of the
spring, and the system is set in motion with initial position = 60
cm and initial velocity = 1.5 m/s.
(a) Find the spring constant.
(b) Write a problem of initial conditions for spring stretching, in meters.
(c) Solve the problem posed in (b).
(d)...

A mass weighing 32 pounds stretches a spring 2 feet. The mass is
initially released from rest from a point 1 foot below the
equilibrium position with an upward velocity of 2ft/sec. find the
equation of the motion and solve it, determine the period and
amplitude.

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...

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