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. 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...
1. A mass of 0.019 kg attached to a spring with spring constant
27.0 N/m is pulled to the right 8.0 cm and released. The mass
oscillates with a frequency of 6.0 Hz. If the mass is pulled to the
right 16.0 cm before being released, what is the frequency?
a. 6.0 Hz
b. 3.0 Hz
c. 1.5 Hz
d. 12 Hz
e. 24 Hz
2. A window loses power/heat energy through a pane of glass to
the cold outside....
a block of mass m=0.10 kg attached to a spring whose spring
constant is k=2.5 N/m . At t=0.2s, the displacement x=-0.3m, and
the velocity v=-2.0m/s
a) find the equation of displacement as a function of time
b) sketch the displacement as a function of time for the first
cycle starting t=0s
When a 5 kg mass is attached to a spring whose constant is
180 N/m, it comes to rest in the equilibrium position. Starting at
t = 0, a force equal to f (t) =
20e−3t cos 6t is applied to
the system. In the absence of damping,
(a)
find the position of the mass when t =
π.
(b)
what is the amplitude of vibrations after a very long time
When a 6 kg mass is attached to a spring whose constant is
24 N/m, it comes to rest in the equilibrium position. Starting at
t = 0, a force equal to f (t) =
42e−7t cos 4t is applied to
the system. In the absence of damping,
(a)
find the position of the mass when t =
π.
(b)
what is the amplitude of vibrations after a very long
time?
When a 6 kg mass is attached to a spring whose constant is
294 N/m, it comes to rest in the equilibrium position. Starting at
t = 0, a force equal to f (t) =
12e−4t cos 3t is applied to
the system. In the absence of damping,
(a)
find the position of the mass when t =
π.
(b)
what is the amplitude of vibrations after a very long
time?
A 1 3 -kg mass is attached to a spring with stiffness 4 N/m. The
damping constant for the system is 2 N-sec/m. The mass is displaced
1 2m to the left and given an initial velocity of 2 m/s to the
right.
(a) Determine the equation of the motion of mass and express it
in the form A e αt sin(βt + φ) by finding the constants A, α, β and
φ in radians.
(b) Find the time t...
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 0.770-kg mass attached to a vertical spring of force constant
147 N/m oscillates with a maximum speed of 0.322 m/s. Calculate the
period related to the motion of the mass. Calculate the amplitude.
Calculate the maximum magnitude of the acceleration.