The Spring Pendulum
Introduction:
The spring pendulum represents a SYSTEM. The system is made up of several COMPONENTS which INTERACT in particular ways. The system can have several STATES.
The spring pendulum is a simple system. We will use it to learn how to understand systems. By itself it is not so interesting, BUT as an example of how to think about systems and how they work it is very important. You are a system, your car is a system, the weather is a system, earth is a system, the universe is a system. EVERYTHING IS A SYSTEM!
Components:
First task -- examine system and take it apart to identify its components.
Q1 - What components of the spring pendulum can you identify?
Spring, Mass, Stand (Rod and Base), Clamp, Hook (connecting mass to spring) --- Missing component - Earth
Q2 - Why is each component important?
Hook and Mass -- Pulls spring down (eventually realize that Earth and mass/earth gravity pull spring down - so earth is a player in the system)
Rod - to hold mass and spring above the base "for all motions of the mass"
Base - to support system in fixed position for all motions of the mass
Clamp - holds the spring and mass near but away from the rod for all motions of the mass
Spring - holds the mass (eventually realize this means produce a force to counter the force of gravity)
DIAGRAM - Mass - force of gravity - no change in motion - balancing force is spring force
Consider other components of system -- are there forces acting here as well? Diagram forces for other components.
Do we understand these forces? We understand (have a model for) gravity. What about the spring force? Spring force seems to change with length of spring.
Investigate the Spring and the Spring force.
Group results -- plot as a class -- Next time hang different masses from spring and measure length - also use spring balance -- suspend spring and pull down with masses or spring balance (Groups divide into teams for these measurements):
States of the System:
Identify states of the system -- (define states of system)
State 1 -- Mass Still (no change in motion of mass)
State 2 -- Mass Oscillating (motion of mass changing)
Time 1 - Bottom, Time 2 - Middle, Time 3 - Top, Time 4 - Middle, Time 5 -Bottom
Q3 - Describe the two states - what is the same, what is different?
Ask what was done to change from one state to second state - see that
primary difference is the change in the MAGNITUDE of the system energy accounts. Energy account in my arm decreased, distortion energy account of spring increased. What about distortion energy of gravity account?
Q4 - What are some behaviors of the system we might want to understand? Select one or two.
IDENTIFY THE SYSTEM BEHAVIOR YOU WANT TO UNDERSTAND.
M - F - E Question:
Q5 - What Mass is important? (how see that the mass of the spring is not important in the simplest picture of the system?)
What Forces are important? - Look at 5 positions above - B,M,T,M,B - remember what you learned about the length of the spring and the spring force.
At first students think gravity "wins" at the bottom and the spring "wins" at the top because it seems they think of the mass as falling (so gravity wins) - we need to get them to see that the object in some sense is already falling because gravity has won at the top and now something needs to stop the mass from falling.
Look at total forces -- find total force is greatest when the mass is at the top and bottom of the motion -- when it is not moving at all - at that time the force is the greatest and the change in motion is the greatest.
What Energy accounts are important?
To answer these questions must examine the states of the system and the behavior (what does the system do) in the various states. Look at behavior of the components, look at the motion of the components, look at the behavior of the forces.
MAKE THE MOST SIMPLE MODEL YOU CAN WHICH FOCUSES ON THE BEHAVIOR YOU WISH TO UNDERSTAND. -- HOW DO WE GET THE STUDENTS TO UNDERSTAND THAT SOME THINGS ARE MORE IMPORTANT THAN OTHER THINGS - THAT SOME THINGS CAN BE NEGLECTED!
Examine Motion in Detail - Model for Motion of Mass:
Measure position vs time -- Bottom, Middle, Top, Middle, Bottom ...
Determine velocity and change in velocity - "acceleration" -- note acceleration looks just like total force as a function of time
Dissipation:
Over time state 2 "Decays" and returns to state 1. What energy accounts are involved in this decay = what energy accounts decrease, what energy accounts increase? -- Air and spring internal energy (thermal energy since material phase of spring not changed) - even if there were no air the decay would still occur and only the thermal energy of the spring would change -- ordered motion of the spring and mass (all atoms moving together up and down) becomes random motion of individual atoms - we can never restore all of this energy into ordered motion.
REVIEW and UNDERSTAND:
1 - What c
2 - What
3 - At what