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How does the attached mass affect the period of oscillation of a vertical…
How does the attached mass affect the period of oscillation of a vertical spring mass system?
Physics Understanding
A spring-mass system can show simple harmonic motion when the displacement is small.
When the mass is pulled down and released, the spring provides a restoring force.
The restoring force acts in the opposite direction to displacement.
The restoring force causes repeated up-and-down motion called oscillation.
The mass oscillates around its equilibrium position.
The key equation is
Independent Variable: Attached Mass
The independent variable is the attached mass.
It is measured in kilograms.
It will be changed using slotted masses.
Mass is suitable because it is easy to measure and change accurately.
Increasing mass is expected to increase the period.
Mass was chosen because it directly appears in the spring-mass period equation.
Possible Values
0.050kg
0.100kg
0.150kg
0.200kg
0.250kg
Dependent Variable: Period of Oscillation
The dependent variable is the period of oscillation.
The period is the time taken for one complete oscillation.
It is measured in seconds.
To improve accuracy, time will be measured for 10 oscillations.
The time for 10 oscillations will be divided by 10.
This reduces the impact of human reaction time.
Formula for data processing:
Period = time for 10 oscillations / 10
Controlled Variables
Spring used must stay the same
Different springs have different spring constants.
Changing the spring would affect the period.
Amplitude of release must stay the same
Large displacements may make the motion less like simple harmonic motion.
2cm will be the fixed release distance
Same release method
Pushing the mass could add extra force.
Releasing sideways could create unwanted motion.
The mass should be released gently without pushing.
Same Number of Oscillations Timed
Timing different numbers of oscillations would make results inconsistent.
Time 10 oscillations for every trial.
Same Clamp Setup
If the clamp moves, the motion may change.
The clamp stand should be stable and kept in the same position.
Hypothesis
The hypothesis is that increasing the attached mass will increase the period of oscillation. This is because a larger mass has a larger inertia. This means that it resists changes in motion and takes longer to complete each oscillation. However, the relationship is not directly proportional.
Feasibility
Equipment is simple and available.
Uses clamp stand, spring, mass hanger, ruler, stopwatch, and slotted masses.
Mass is easy to manipulate.
Period is easy to measure.
The experiment is safe if the mass range is controlled.
The investigation can be completed in class time.
Risks
Falling masses could injure feet.
Spring recoil could hit someone.
Clamp stand could tip over.
Spring could be overstretched.
Solutions
Secure masses properly and wear solid shoes.
Use small displacement and do not overstretch the spring.
Use a stable bench and ensure the clamp is tightened.
Use a safe mass range and avoid going past the elastic limit.
Justification for choosing mass
Mass directly appears in the spring-mass period equation.
It has a clear theoretical relationship with period.
It is easier to control than spring constant or air resistance.
It is safer and more practical to change than using different springs.
It allows a clear comparison between theory and experiment.
It is suitable under school lab conditions.
Other Factors Involved
Spring constant
Amplitude of release
Release method
Air resistance
Friction at support point
Sideways motion
Timing accuracy
Elastic limit of spring
