Question

Consider a horizontal spring-mass vibration system without damping, where the mass is 2 kg, the spring is 18 N/m, and the external force is a periodic force f(t) = 6sin(3t):

a) Write the differential equation modeling the motion of this spring-mass system

b) Solve the differential equation in (a). Show Work

c) If at the initial time t = 0, the mass is at position 2 m to the right of the equilibrium position and its velocity is 1 m/s moving towards the left, find a particular equation y(t) that describes the position of the mass at time t.

Answer #1

consider a spring mass system with a damping force but no
external force that has the following equation of motion. Find the
damping constant c that gives the critical damping
x'+cx'+9x=0 x(0)=2 x'(0)=0

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 resistance numerically equal to the
magnitude of the instantaneous velocity.
(a) If the system is driven by an external force of (12 cos 3t −
8 sin 3t) N, determine the steady-state response.
(b) Find the gain function if the external force is f(t) =
cos(ωt).
(c) Verify...

when a mass of 2 kg is attached to a spring whose constant is 32
N/m, it come to rest in the equilibrium position. at a starting
time t=0, an external force of y=80e^(-4t)*cos(4t) is applied to
the system. find the motion equation in the absence of damping.

A 1/2 kg mass is attached to a spring with 20 N/m. The
damping constant for the system is 6 N-sec/m. If the mass is moved
12/5 m to the left of equilibrium and given an initial rightward
velocity of 62/5 m/sec, determine the equation of motion of the
mass and give its damping factor, quasiperiod, and
quasifrequency.
What is the equation of motion?
y(t)=
The damping factor is:
The quasiperiod is:
The quasifrequency is:

A
mass of 1kg stretches a spring by 32cm. The damping constant is
c=0. Exterbal vibrations create a force of F(t)= 4 sin 3t Netwons,
setting the spring in motion from its equilibrium position with
zero velocity. What is the coefficient of sin 3t of the
steady-state solution? Use g=9.8 m/s^2. Express your answe is two
decimal places.

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).
R=
ω=
δ=

A mass m is
attached to a spring with stiffness k=25 N/m. The mass is stretched
1 m to the left of the equilibrium point then released with initial
velocity 0.
Assume that m = 3 kg, the damping force is negligible,
and there is no external force. Find the position of the mass at
any time along with the frequency, amplitude, and phase angle of
the motion.
Suppose that the spring is immersed in a fluid with damping
constant...

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 mass weighing 16 pounds stretches a spring
8
3
feet.
The mass is initially released from rest from a point
3 feet
below the equilibrium position, and the subsequent motion takes
place in a medium that offers a damping force that is numerically
equal to
1
2
the
instantaneous velocity. Find the equation of motion
x(t)
if
the mass is driven by an external force equal to
f(t) = 20 cos(3t).
(Use
g =
32 ft/s2
for
the acceleration...

A mass weighing 16 pounds stretches a spring 8 3 feet. The mass
is initially released from rest from a point 3 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 1 2
the instantaneous velocity. Find the equation of motion x(t) if the
mass is driven by an external force equal to f(t) = 10 cos(3t).
(Use g = 32 ft/s2 for the acceleration...

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