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Simulation Setup:
Simulation Setup:
Turn on the following lines:
Displacement/Natural Length
Equilibrium Point
Movable Line
Set Damping to ZERO
As the mass moves, when is the kinetic energy at its maximum? When is it at its minimum?
When is the elastic potential energy (spring energy) at its maximum? When is it at its minimum?
How do kinetic and potential energy trade off throughout the oscillation? Is there a point where they are equal?
Describe what happens to the total mechanical energy of the system if there is no damping. Does it stay constant? Why?
What happens to the energy if you turn on damping? How does this relate to real-world oscillations?
How does increasing the mass affect the period of oscillation?
How does changing the spring constant (k) affect the motion of the mass?
Based on your observations, what equation might describe the period of oscillation? (Hint: Consider Hooke’s Law and Newton’s Second Law.)
If you double the amplitude of oscillation, does the period change? Why or why not?
Where do you see similar energy transformations happening in real life (e.g., trampolines, diving boards, car suspensions)?
How could damping be useful or problematic in real-world systems? Can you think of situations where you would want to increase or decrease damping?
At what point is the pendulum’s kinetic energy at its maximum? When is it at its minimum?
At what point is the pendulum’s gravitational potential energy at its maximum? When is it at its minimum?
How does the total mechanical energy of the pendulum change over time when there is no damping?
What happens to the pendulum’s energy when damping is introduced? How does this relate to real-world scenarios?
How does changing the length of the pendulum affect the period of oscillation?
Does the mass of the pendulum bob affect the period? Why or why not?
If you double the initial amplitude (release height), does the period change? Why or why not?
What happens if you release the pendulum at an extremely large angle (close to 90°)? How does the motion differ from when it starts at a small angle?
Where do you see pendulums in real life? How do they demonstrate energy transformations?
Why do grandfather clocks and metronomes rely on pendulums? How does damping affect their operation?
How could damping be useful in some real-world applications (e.g., engineering, earthquake-proofing buildings)?
What conditions would need to be met for a pendulum to act as a perfect simple harmonic oscillator?
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