Harmonic Motion Lab
Lab Partner: Macauley
Kinematics
Movement of the Object: The object, a 500g weight, travels in simple harmonic motion and oscillates.
Simple harmonic motion occurs when the displacement of an object is directly proportional to the force
that is acting on the object, in this case the spring. The object also oscillates. Oscillation is when an object
moves back and forth and returns to its original position in a period of time. A period is the length of time it
takes for an object to complete one cycle. In this lab, as time increases, the period decreases.This means
that as time increases, the length of time it takes for the object to return to its original position decreases.
Simple harmonic motion occurs when the displacement of an object is directly proportional to the force
that is acting on the object, in this case the spring. The object also oscillates. Oscillation is when an object
moves back and forth and returns to its original position in a period of time. A period is the length of time it
takes for an object to complete one cycle. In this lab, as time increases, the period decreases.This means
that as time increases, the length of time it takes for the object to return to its original position decreases.
![Picture](/uploads/3/8/7/7/38773679/2885119.jpg?463)
Position vs Time
This position vs time graph displays one period.
A period, which is one cycle, can begin from any
point as long as it concludes at the same point.
All of the graphs display data relative to the
y-axis/height of the object. The position vs time
graph proves that the object is oscillating
because the height decreases and then
increases again within a period.
This position vs time graph displays one period.
A period, which is one cycle, can begin from any
point as long as it concludes at the same point.
All of the graphs display data relative to the
y-axis/height of the object. The position vs time
graph proves that the object is oscillating
because the height decreases and then
increases again within a period.
![Picture](/uploads/3/8/7/7/38773679/2070138.jpg?469)
Velocity vs Time
The velocity of the object is not constant and
this can be proved using the graph as evidence.
The period of the graph is about 0.8 seconds
and within that time, there is a wide change in
velocity where it increases and decreases. For
an object to stay in constant velocity, it must
either not be moving or move at a constant
speed.If the object was moving at a constant
velocity, the line on the graph would also be
linear.
![Picture](/uploads/3/8/7/7/38773679/1412534926.png)
Acceleration vs Time
The acceleration varies at different times in the
graph. The acceleration is greatest around 0.33
seconds and lowest in the beginning and end
of the period. Our prediction is that the height
of the object affects the acceleration. When the
object is at the lowest height and the spring is
stretched out the most, the acceleration is
greater. As the object gets closer to the spring
and gains height, the acceleration gradually
drops. Newton's first law implies that when
acceleration is 0 then the forces are balanced.
We can see that most of the time the forces are
unbalanced with the exception of a split second
where acceleration is 0.
The acceleration varies at different times in the
graph. The acceleration is greatest around 0.33
seconds and lowest in the beginning and end
of the period. Our prediction is that the height
of the object affects the acceleration. When the
object is at the lowest height and the spring is
stretched out the most, the acceleration is
greater. As the object gets closer to the spring
and gains height, the acceleration gradually
drops. Newton's first law implies that when
acceleration is 0 then the forces are balanced.
We can see that most of the time the forces are
unbalanced with the exception of a split second
where acceleration is 0.
What is a Spring Constant?
Spring constant is a property of a spring which defines its flexibility or in other
terms,how much the springwill stretch. Spring constant can be found using the
formula: T= 2π x √(m/k). T stands for time, m stands for the mass of the object, and k
stands for the spring constant. To algebraically solve for k, we have to rearrange the
variables to end up with a new equation: K= (4π²m)/T².
Spring constant is a property of a spring which defines its flexibility or in other
terms,how much the springwill stretch. Spring constant can be found using the
formula: T= 2π x √(m/k). T stands for time, m stands for the mass of the object, and k
stands for the spring constant. To algebraically solve for k, we have to rearrange the
variables to end up with a new equation: K= (4π²m)/T².
Calculation of Spring Constant:
Equation: K= (4π²m)/T²
K= (4xπ²x0.5 kilograms)/(o.80)²seconds
K= 19.7 kilograms/ 0.64 seconds²
Spring Constant = 30.8 N/M
K= (4xπ²x0.5 kilograms)/(o.80)²seconds
K= 19.7 kilograms/ 0.64 seconds²
Spring Constant = 30.8 N/M
Forces
![Picture](/uploads/3/8/7/7/38773679/1413145931.png)
The object is at the highest position when the force of the spring
(Fspring) pulling up on it is very small compared to the force of
gravity(Fg) pulling down on it. This will result in the object being pulled
downward once more.
Spring's Force
To find the Spring's Force we have to do more rearranging:
Ftotal = Fspring - Fgravity
Fspring = Ftotal + Fgravity
Newton's Second Law: Force = Mass x Acceleration
Mass: 0.50 kilograms
Acceleration: -1.75 m/s²
Ftotal =0.50 kilograms x -1.75 m/s²
Ftotal= -0.875 N
Force of Gravity
Force = Mass x Acceleration
The acceleration of gravity is 9.8 m/s² .
Fgravity = 0.50 kilograms x 9.8 m/s²
Fgravity = 4.9 N
Fspring = -0.875 N + 4.9 N
Fspring = 4.025 N
(Fspring) pulling up on it is very small compared to the force of
gravity(Fg) pulling down on it. This will result in the object being pulled
downward once more.
Spring's Force
To find the Spring's Force we have to do more rearranging:
Ftotal = Fspring - Fgravity
Fspring = Ftotal + Fgravity
Newton's Second Law: Force = Mass x Acceleration
Mass: 0.50 kilograms
Acceleration: -1.75 m/s²
Ftotal =0.50 kilograms x -1.75 m/s²
Ftotal= -0.875 N
Force of Gravity
Force = Mass x Acceleration
The acceleration of gravity is 9.8 m/s² .
Fgravity = 0.50 kilograms x 9.8 m/s²
Fgravity = 4.9 N
Fspring = -0.875 N + 4.9 N
Fspring = 4.025 N
![Picture](/uploads/3/8/7/7/38773679/1686534.png?265)
The object is at equilibrium when the force of the spring pulling up
on it (Fspring) and the force pulling down on it (Fg), which stands
for gravity, are both equal. This occurs for a very short period in the
lab when the object travels at a constant velocity for a very short period.
Spring's Force
To find the Spring's Force we have to do more rearranging:
Ftotal = Fspring - Fgravity
Fspring = Ftotal + Fgravity
Newton's Second Law: Force = Mass x Acceleration
Mass: 0.50 kilograms
Acceleration: 0 m/s²
Ftotal = 0.50 kilograms x 0 m/s²
Ftotal = 0 N
Force of Gravity
Force = Mass x Acceleration
The acceleration of gravity is 9.8 m/s²
Fgravity = 0.50 kilograms x 9.8 m/s²
Fgravity = 4.9 N
Fspring = 0 N + 4.9 N
Fspring = 4.9 N
on it (Fspring) and the force pulling down on it (Fg), which stands
for gravity, are both equal. This occurs for a very short period in the
lab when the object travels at a constant velocity for a very short period.
Spring's Force
To find the Spring's Force we have to do more rearranging:
Ftotal = Fspring - Fgravity
Fspring = Ftotal + Fgravity
Newton's Second Law: Force = Mass x Acceleration
Mass: 0.50 kilograms
Acceleration: 0 m/s²
Ftotal = 0.50 kilograms x 0 m/s²
Ftotal = 0 N
Force of Gravity
Force = Mass x Acceleration
The acceleration of gravity is 9.8 m/s²
Fgravity = 0.50 kilograms x 9.8 m/s²
Fgravity = 4.9 N
Fspring = 0 N + 4.9 N
Fspring = 4.9 N
![Picture](/uploads/3/8/7/7/38773679/1413145992.png)
The object is at its lowest position when there isn't much gravitational
force, but the force of the spring is high. This will result in the object
moving in an upward motion.
Spring's Force
To find the Spring's Force we have to do more rearranging:
Ftotal = Fspring - Fgravity
Fspring = Ftotal + Fgravity
Newton's Second Law: Force = Mass x Acceleration
Mass: 0.50 kilograms
Acceleration: 1.82 m/s²
Ftotal = 0.50 kilograms x 1.82 m/s²
Ftotal = 0.91 N
Force of Gravity
Force = Mass x Acceleration
The acceleration of gravity is 9.8 m/s²
Fgravity = 0.50 kilograms x 9.8 m/s²
Fgravity = 4.9 N
Fspring = 0.91 N + 4.9 N
Fspring = 5.81 N
force, but the force of the spring is high. This will result in the object
moving in an upward motion.
Spring's Force
To find the Spring's Force we have to do more rearranging:
Ftotal = Fspring - Fgravity
Fspring = Ftotal + Fgravity
Newton's Second Law: Force = Mass x Acceleration
Mass: 0.50 kilograms
Acceleration: 1.82 m/s²
Ftotal = 0.50 kilograms x 1.82 m/s²
Ftotal = 0.91 N
Force of Gravity
Force = Mass x Acceleration
The acceleration of gravity is 9.8 m/s²
Fgravity = 0.50 kilograms x 9.8 m/s²
Fgravity = 4.9 N
Fspring = 0.91 N + 4.9 N
Fspring = 5.81 N
Force vs Time graph
The force vs time graph shows how force increases and decreases as time goes on. It is obvious that the forces are not constant throughtout the period. This graph is very similar to the acceleration graph. Acceleration and force both seem to increase as the object's height decreases. They are directly proportional. |
Energy
![Picture](/uploads/3/8/7/7/38773679/6955933.jpg?421)
Kinetic Energy vs Time
Kinetic energy and time are related through the
position and movement of the object. The object has
the greatest kinetic energy when it is traveling
downward and upward after it has hit it's maximum
and minimum points. The two peak points in the
graph represent the object as it moves down and
then moves up.
Kinetic energy and time are related through the
position and movement of the object. The object has
the greatest kinetic energy when it is traveling
downward and upward after it has hit it's maximum
and minimum points. The two peak points in the
graph represent the object as it moves down and
then moves up.
![Picture](/uploads/3/8/7/7/38773679/796107.jpg?419)
Potential Energy vs Time
Potential energy is the stored energy possessed by
an object. The potential energy is highest when the
object is at the highest point and it is the lowest
when the object is at its lowest point. Height affects
potential energy because the fromula for it is mass x
gravitational pull x height. In this situation, the mass
and gravitational pull are constant, so the only
variable that changes is the height. In conclusion,
potential energy increases as height increases.
Potential energy is the stored energy possessed by
an object. The potential energy is highest when the
object is at the highest point and it is the lowest
when the object is at its lowest point. Height affects
potential energy because the fromula for it is mass x
gravitational pull x height. In this situation, the mass
and gravitational pull are constant, so the only
variable that changes is the height. In conclusion,
potential energy increases as height increases.
![Picture](/uploads/3/8/7/7/38773679/8592071.jpg?854)
Total Mechanical Energy vs Time
Mechanical energy is defined as the energy of an object relative to its motion or position. This includes
both kinetic and potential energy. The mechanical energy increases as the kinetic energy increases
because the mechanical energy is the kinetic energy added to the potential energy. The potential energy
also has an effect. As the mechanical energy goes down the potential energy also goes down. It is not a
straight line because while the the spring is constantly moving, the kinetic energy stays the same but the
potential energy decreases then increases again so the mechanical energy also decreases then increases
during one period.
Mechanical energy is defined as the energy of an object relative to its motion or position. This includes
both kinetic and potential energy. The mechanical energy increases as the kinetic energy increases
because the mechanical energy is the kinetic energy added to the potential energy. The potential energy
also has an effect. As the mechanical energy goes down the potential energy also goes down. It is not a
straight line because while the the spring is constantly moving, the kinetic energy stays the same but the
potential energy decreases then increases again so the mechanical energy also decreases then increases
during one period.
Kinetic Energy for Entire Motion
The kinetic energy of the entire motion proves an important aspect to the lab. We see the as time increases
the amount of kinetic energy is slowly decreasing. This energy is being transferred elsewhere. Eventually,
the maximum point of each period will get lower and lower until the object stops moving.
The kinetic energy of the entire motion proves an important aspect to the lab. We see the as time increases
the amount of kinetic energy is slowly decreasing. This energy is being transferred elsewhere. Eventually,
the maximum point of each period will get lower and lower until the object stops moving.