Question

You hang a 300 g mass on a spring.

a. If the spring initially stretches 6.20 cm when you hang the mass
on it, what is the spring constant?

b. How long will one oscillation take?

The spring is now oriented horizontally and attached to a glider on
a frictionless air track. The glider also has a mass of 300g. You
want to observe the oscillations of this spring-mass system in the
lab with a motion detector. You stretch the spring so that the mass
is 2.0 cm to the right of its equilibrium position and release it.
You then push the start on the motion detector, but the delay is
such that the mass is now 1.0 cm to the left of the equilibrium
position and moving to the right at time t=0.0 s on the detector
output. For the next part, use clearly labeled numerical
axes.

c. Draw a position vs time graph of the mass for two cycles of the
motion. Choose the equilibrium position as x=0 and the first moment
the detector records as t=0.

d. Draw a velocity vs. time graph of the mass for two cycles of the
motion.

e. Draw an acceleration vs. time graph of the mass for two cycles
of the motion.

f. On each graph, draw a circle around the points where the Kinetic
Energy of the system is zero.

g. On each graph draw a square around the points where the
Potential Energy of the system is a minimum.

h. If you replace the original glider with a 600 g glider, what
will be the frequency of oscillations for this new mass/spring
system?

Please answer e,f,g,h

Answer #1

Finding the Spring Constant
We can describe an oscillating mass in terms of its position,
velocity, and acceleration as a function of time. We can also
describe the system from an energy perspective. In this experiment,
you will measure the position and velocity as a function of time
for an oscillating mass and spring system, and from those data,
plot the kinetic and potential energies of the system.
Energy is present in three forms for the mass and spring system....

You hang a 400 gram mass on a spring and the spring stretches
16.0 cm. You then pull the mass down an additional 4.0 cm and let
it go.
a) Write an equation for the position of the mass as a function
of time.
b) Where will the mass be located 4.0 seconds later?
c) What will its velocity be?

A spring has an unstretched length of 10 cm. When a 150 g mass
is added the spring stretches to a total
length of 15 cm, where the mass rests at equilibrium.
What is the spring constant of the spring?
Now the mass is pulled down by an additional 5 cm, so that the
total length of the spring is 20 cm,
and then released. What is the frequency and period of the
subsequent oscillation?
Draw a graph—including numbers on...

A spring has an unstretched length of 10 cm. When a 150 g mass
is added the spring stretches to a total length of 15 cm, where the
mass rests at equilibrium.
A. What is the spring constant of the spring?
B. Now the mass is pulled down by an additional 5 cm, so that
the total length of the spring is 20 cm, and then released. What is
the frequency and period of the subsequent oscillation?
C. Draw a...

A spring has an unstretched length of 10 cm. When a 150 g mass
is added the spring stretches to a total length of 15 cm, where the
mass rests at equilibrium.
A. What is the spring constant of the spring?
B. Now the mass is pulled down by an additional 5 cm, so that
the total length of the spring is 20 cm,and then released. What is
the frequency and period of the subsequent oscillation?
C. Draw a graph—including...

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...

A mass of 100 g stretches a spring 1.568 cm. If the mass is set
in motion from its equilibrium position with a downward velocity of
40 cms, and if there is no damping, determine the position u of the
mass at any time t.
Enclose arguments of functions in parentheses. For example,
sin(2x).

A particle with mass 2.61 kg oscillates horizontally at the end
of a horizontal spring. A student measures an amplitude of 0.923 m
and a duration of 129 s for 65 cycles of oscillation. Find the
frequency, ?, the speed at the equilibrium position, ?max, the
spring constant, ?, the potential energy at an endpoint, ?max, the
potential energy when the particle is located 68.5% of the
amplitude away from the equiliibrium position, ?, and the kinetic
energy, ?, and...

A spring-mass system consists of a 0.5 kg mass attached to a
spring with a force constant of k = 8 N/m. You may neglect the mass
of the spring. The system undergoes simple harmonic motion with an
amplitude of 5 cm. Calculate the following: 1. The period T of the
motion 2. The maximum speed Vmax 3. The speed of the object when it
is at x = 3.5 cm from the equilibrium position. 4. The total energy
E...

A spring-mass system is composed of
a mass m = 200 g and a massless spring of force
constant k obeying Hooke’s Law, and the whole system is
located on a horizontal frictionless table. The mass m
makes oscillations about the equilibrium position x = 0
according to the relation x(t) = (15 cm)
sin 2πt. (You can take π = 3.)
What is the force constant k of the spring?
(a) 36/5
N/m (b) 36 N/m (c) 54
N/m ...

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