Interactive Lecture Demonstration
Prediction
Sheet—Simple Harmonic Motion
Directions: Click here to download the Prediction Sheet. Write your name at the top to record your
presence and participation in these demonstrations. Be sure to always make predictions before
observing the results. Your instructor
may ask you to send this sheet in.
Demonstration
1:
We'll use a small cart that can oscillate between two springs. You can view
the cart and springs by clicking here. The
cart is interfaced with a computer that collects motion and force data as it
oscillates. Its motion is started by pulling it to one side of its
equilibrium position and releasing it. The displacement is zero whenever the
cart is at its equilibrium position. You can download and view a video of the
motion by clicking here. (Note that because of
friction in the wheels, the amplitude of the motion decreases in time.) The force exerted on the cart by the
springs is proportional to the displacementthe distance from the
equilibrium point. Demonstration 1: Watch the motion of the cart in the video
and sketch on the axes on the right your predictions of the graphs of force
vs. time, displacement vs. time, velocity vs. time, and acceleration vs.
time. Be sure to carefully sketch the time relationship between the four
quantities you are graphing. Only after you
have made your predictions, click here to
download a video showing the motion and the collected graphs. You can also
download just the graphs by clicking here. Answer the following questions based on
the graphs. A. What is the shape of the displacement
vs. time graph? Do the other three graphs have a similar shape? B. Find a positive maximum of the
displacement. Are the maxima of velocity at the same times? If not what
fraction of a period is the difference in time for the displacement and
velocity maxima? Explain this difference in terms of the motion. When the
cart is at its maximum displacement, what is the velocity? C. Find a positive maximum of the displacement.
Are the positive maxima of acceleration at the same times? If not what
fraction of a period is the difference in time for the displacement and
velocity maxima? Explain this difference in terms of the motion. When the
cart is at its maximum displacement, what is the acceleration? When the cart
is at its equilibrium position, what is the acceleration?
D. Compare the forcetime graph to the
accelerationtime graph. How are they
similar? How different? What is the relationship between force and
acceleration? Is the force ever zero?
If so, at what point in the motion? 


Demonstration
2:
Suppose that you wanted to model the motion (displacement) of the cart
between two springs by writing down a mathematical expression for
displacement vs. time. What
mathematical expression would you use?
What additional measurements would you need to make so that the
expression would exactly represent the motion? Only after you have made your
prediction, click here to see a possible mathematical
expression representing the motion. 


For
Demonstrations 35, you will be considering the motion of a mass (actually
the same cart) suspended vertically from a spring. You can observe this
motion by clicking here to download and view
the video. 


Demonstration
3: Suppose that increase the amplitude of the
oscillation by pulling down the cart further below equilibrium before
releasing it. Predict what effect this will have on the period and frequency
of the motion. Only after you have made your
prediction, click here to download a video
and view the motion and a graph. You can also click here to view just the graph. Did increasing the amplitude of the
oscillation affect the period and frequency? If yes, describe the change. 


Demonstration
4: Suppose that increase the spring constant by
suspending the cart with two springs next to each other. Predict what effect
this will have on the period and frequency of the motion. Only after you have made your
prediction, click here to download a video
and view the motion and a graph. You can also click here to view just the graph. Did increasing the spring constant
affect the period and frequency? If yes, describe the change. 


Demonstration
5:
Suppose that increase the mass by hanging some weights from the bottom of the
cart. Predict what effect this will have on the period and frequency of the
motion. Only after you have made your
prediction, click here to download a video
and view the motion and a graph. You can also click here to view just the graph. Did increasing the mass affect the
period and frequency? If yes, describe the change. 

