Download Springs Virtual Lab

- Virtual Lab -
Simple Harmonic Motion
of an Oscillating Spring
http://www.walter-fendt.de/html5/phen/springpendulum_en.htm
This Java applet demonstrates the variation of elongation, velocity, acceleration,
force and energy during the oscillation of a spring pendulum (assumed with no
friction).
The "Reset" button brings the body of pendulum to its initial position. You can
start or stop and continue the simulation with the other two buttons. If you
choose the option "Slow Motion", the movement will be five times slower. The
spring constant, the mass and the amplitude of the oscillation can be changed
within certain limits. In order to select another physical size you have to click on
the appropriate one of the five radio buttons.
Hooke’s Law: Whenever a spring is stretched from its equilibrium position and
released, it will move back and forth on either side of the equilibrium position.
The force that pulls it back and attempts to restore the spring to equilibrium is
called the restoring force. It magnitude can be written as
Restoring Force = (force constant)(displacement form equilibrium) or F = - ky
This relationship is known as Hooke’s Law. The force constant is a measure of
the stiffness of the spring. The Metric unit for the force constant is the newton
per meter (N/m). A spring with a force constant of 400 N/m requires a force of
400-N to stretch it a distance of one meter.
Keep in mind that the restoring force is the force needed to bring the spring back
to its original position. The force that acts to move the spring away from the
equilibrium position is equal in magnitude to the restoring force, but opposite in
direction.
Simple Harmonic Motion is motion that occurs when the restoring force acting on
an object is proportional to the object’s displacement from its rest position, but
opposite in direction (F = -ky) . Objects at the end of springs move in simple
harmonic motion when they are displaced from their rest position and bounce up
and down on the spring, or oscillate at a constant frequency or period. This
motion in able to produce a sine wave as seen in the simulation graphs.
The Oscillation Period (T) is a measure of the time for the mass to complete one
cycle that can be determined using the graphic display of the simulation. The
frequency (f) of the oscillating mass is a measure of the number of cycles per
second ( or hertz). The frequency can be determined as it is the reciprocal of
the period (T).
f = 1/T
Investigation #1
What factors affect the Period (frequency) of an Oscillating Pendulum?
Procedure:

Open the browser to the Oscillating Pendulum web site:
http://www.walter-fendt.de/ph11e/springpendulum.htm


Notice you have the ability to adjust the value of the spring constant
(spring stiffness), mass (attached to the bottom of the spring and pulling
the spring downward), and amplitude (maximum distance the mass
moves from the equilibrium position) of the spring pendulum. Complete
the data table below to determine which alter the Oscillation Period of the
pendulum and calculate the frequency of the spring pendulum.
Predict which of these you feel may alter the period or time for one
complete cycle. Underline your choice(s): Spring Constant, Mass,
Amplitude.
Changing the Mass
Mass
Spring
Constant
Amplitude
Period
Frequency
(kg)
(N/m)
(m)
(s)
(Hz =
cycles/s)
1.0
20
0.05
3.0
20
0.05
7.0
20
0.05
10.0
20
0.05
Does changing the mass alter the period or frequency?
Changing the Spring Constant
Mass
Spring
Constant
Amplitude
Period
Frequency
(kg)
(N/m)
(m)
(s)
(Hz =
cycles/s)
5.0
10
0.05
5.0
20
0.05
5.0
30
0.05
5.0
50
0.05
Does changing the Spring Constant alter the period or frequency?
Changing the Amplitude
Mass
Spring
Constant
Amplitude
(kg)
(N/m)
(m)
5.0
20
0.01
5.0
20
0.04
5.0
20
0.08
5.0
20
0.10
Period Frequency
(s)
(Hz =
cycles/s)
Does changing the Amplitude alter the period or frequency?
Investigation #2
Understanding this Simple Harmonic Motion
When an object experiences Simple Harmonic Motion the force, velocity,
acceleration, and conversion of energy need to be studied for a complete
understanding. Simple Harmonic Motion is motion that is caused by a restoring
force that is directed toward the equilibrium position of the oscillating object.
This restoring force and the inertia of the object cause the object to vibrate
about its equilibrium position. This simulation assumes no resistance to the
oscillating motion of the mass connected to the spring.
Procedure:
Investigation of Elongation - What is it?




1.
2.
3.
4.
Press the "reset" button on the simulation.
Select a mass of 2 kilograms, spring constant of 20 N/m, and an
elongation of 0.05 m.
Select "slow motion" whenever you wish to reduce the rate at which the
simulation runs for the purpose of a closer analysis of the motion.
Press the "elongation" button followed by pressing the "start" button.
What is displayed in the animation to represent the elongation?
What is the definition of elongation?
How many complete cycles are shown on the graph?
When the graph shows a positive elongation is the mass above or below
the equilibrium position?
Investigation of Velocity of the mass





Press the "reset" button on the simulation.
Select a mass of 2 kilograms, spring constant of 20 N/m, and an
elongation of 0.05 m.
Select "slow motion" whenever you wish to reduce the rate at which the
simulation runs for the purpose of a closer analysis of the motion.
Press the "Velocity" button followed by pressing the "start" button.
The velocity vector is shown in the animation of the moving mass. When
the speed is greatest the arrow length is greatest. When the speed is
zero the arrow disappears.
1. In terms of elongation, when is the velocity equal to 0.0 m/s?
2. In terms of elongation, when is the velocity greatest?
3. When does the moving mass having a positive velocity? Negative
velocity?
4. Will changing the mass alter the maximum velocity?
If so, will more mass increase the velocity?
5. Will changing the spring constant alter the maximum velocity?
If so, will a larger spring constant increase the velocity?
6. Will changing the amplitude alter the maximum velocity?
If so, will a larger amplitude increase the maximum velocity?
Investigation of Acceleration of the mass





Press the "reset" button on the simulation.
Select a mass of 2 kilograms, spring constant of 20 N/m, and an
elongation of 0.05 m.
Select "slow motion" whenever you wish to reduce the rate at which the
simulation runs for the purpose of a closer analysis of the motion.
Press the "Acceleration" button followed by pressing the "start" button.
The acceleration vector is shown in the animation of the moving mass.
When the acceleration is greatest the arrow length is greatest. When the
acceleration is zero the arrow disappears.
1. In terms of elongation, when is the acceleration equal to 0.0 m/s?
2. In terms of elongation, when is the acceleration greatest?
3. When does the moving mass having a positive acceleration? Negative
acceleration?
4. Will changing the mass alter the maximum acceleration? If so, will more
mass increase the acceleration?
5. Will changing the spring constant alter the maximum acceleration?
If
so, will a larger spring constant increase the acceleration?
6. Will changing the amplitude alter the maximum acceleration?
If so, will
a larger amplitude increase the maximum acceleration?
Investigation of the Force acting on the mass





Press the "reset" button on the simulation.
Select a mass of 2 kilograms, spring constant of 20 N/m, and an
elongation of 0.05 m.
Select "slow motion" whenever you wish to reduce the rate at which the
simulation runs for the purpose of a closer analysis of the motion.
Press the "Force" button followed by pressing the "start" button.
The Force vector is shown in the animation of the moving mass. When
the Force is greatest the arrow length is greatest. When the Force is zero
the arrow disappears.
In terms of elongation, when is the Force equal to 0.0 N?
In terms of elongation, when is the Force greatest?
When does the moving mass having a positive Force? Negative Force?
Will changing the mass alter the maximum Force?
Will changing the spring constant alter the maximum Force?
If so, will a larger spring constant increase the Force?
6. Will changing the amplitude alter the maximum Force?
7. If so, will a larger amplitude increase the maximum Force?
1.
2.
3.
4.
5.
Investigation of Energy Conversions: Potential and Kinetic Energy




Press the "reset" button on the simulation.
Select a mass of 2 kilograms, spring constant of 20 N/m, and an
elongation of 0.05 m.
Select "slow motion" whenever you wish to reduce the rate at which the
simulation runs for the purpose of a closer analysis of the motion.
Press the "Energy" button followed by pressing the "start" button.
The potential energy of the spring is called elastic potential energy. Energy is
stored in a spring when it is stretched or compressed beyond its equilibrium
position.
1.
2.
3.
4.
5.
When does the moving mass have the maximum kinetic energy?
When is the kinetic energy minimum (0.0 joules)?
When is the elastic potential energy at a maximum value?
When is the elastic potential energy a minimum (0.0 joules)?
Does the total energy in the system change as the mass oscillates?
In Summary:
Write a brief report on the main ideas of Simple Harmonic Motion and the
Oscillation of a pendulum. (State what you know/learned by doing this virtual
lab.)