Physics 12 Gizmo Period of Mass on a Spring

Physics 12 Gizmo – Period of Mass on a Spring

Next time you see a child bouncing on a pogo stick, take a moment to ponder the frequency with which they bounce. You could check this by counting the number of bounces that they complete within a period of, say, fifteen seconds or so.

If the child gives the pogo stick to a bigger, heavier friend, an interesting thing will occur. The heavier friend will complete fewer bounces in the same fifteen seconds than the first child.

How can we explain the tale of the two children and the pogo stick? Studying an oscillating spring with a mass on the end of it can help.

The Period of the System

In this activity, you will examine an oscillating system made up of a mass attached to a spring, and determine the period of the system.

1. In the Gizmo™, observe the oscillating mass-spring system. (Note that you can vary the speed of the simulation in the DESCRIPTION if you like.)

a. What is the lowest point that the oscillating mass reaches? What is its highest point?

b. Practice clicking the Mark time button each time the mass reaches its lowest point. Do this at least five times or so, until you have the hang of it. You will use this in the next step.

2. Click the TABLE tab. Click Reset to clear the table. In this step, you will "mark time" to make an estimate for the period of this mass-spring system. When you are ready to start, click Mark time when the mass reaches its lowest point. Continue to click on Mark time each time the mass reaches its low point. Do this for a total of about twelve oscillations of the system. The times in the table represent the time between successive clicks on Mark time.

a. Compare the values for Time between clicks in the table. (Ignore the first value.) Does the period of the system appear to change over time, or does it remain constant? Justify your answer based on your data.

b. Ignore the first time in the list and average the remaining values. What is the average duration for an oscillation of this system? This is your estimate for the period of the oscillation.

c. If you only averaged two or three observations of Time between clicks instead of twelve, do you think you would have a better or worse estimate for the period of the system? Explain.

d. If you averaged 100 observations, do you think you would have a better or worse estimate for the period? What about 1000 observations? What is the obvious problem with doing this many observations?

Factors Affecting the Period In this activity, you will examine the effect that changing the mass (m), the stiffness of the spring (k), or the acceleration due to gravity (g) has on the period of the system.

1. Check that the k and g sliders below the spring are set to their default values, k = 100.0 N/m, and g = 9.8 m/s 2 . (To quickly set a slider to a specific value, type the number in the field to the right of the slider and press Enter.) The value g = 9.8 m/s 2 is a popular value for acceleration due to gravity, because that is the value on Earth.

a. Set m, the mass on the spring, to 0.5 kg. What do you notice about the spring? Does it reach as low as before? Explain why you think this is.

b. Be sure the TABLE pane is visible. If any values are already displayed in the table, click Reset. When the mass reaches its lowest point, click on Mark time. (Note: If the spring is moving to fast, you can slow the simulation with the Simulation speed slider on the DESCRIPTION tab.) Continue to click on Mark time each time the mass reaches its low point for about twelve more oscillations of the system. Ignore the first time in the list and average the remaining values. What is the period for an oscillation of this system?

c. Increase m to 2.0 kg, and leave the other values unchanged. How does this change the motion of the spring?

d. Using the same procedure, determine the period of the oscillating system. What is the period? How does the period compare to the period when the mass was 0.5 kg? (What value was the period multiplied or divided by?) What was the value of m multiplied by?

e. You should have found that, when you multiplied m by 4, the period was multiplied by 2. Now, compare the average periods when the mass is 0.2 kg and 1.8 kg. When you multiplied m by 9, what was the period multiplied by?

f. Measure the period when m is 0.1 kg. Now, based on the patterns you have seen so far, predict the period when the mass is multiplied by 16 (m = 1.6 kg). Use the Gizmo to check your answer. If you were correct, describe a general rule to summarize how changing the mass affects the period. If possible, discuss your response with your teacher and classmates.

2. Return the sliders to their default values, (m = 1.0 kg, k = 100 N/m and g = 9.8 m/s 2 ). Using a procedure similar to that from step 1, determine the period of the system for five different values of k, the spring constant. (The spring constant is a measure of the stiffness of the spring. The stiffer the spring, the higher the value of k.) Remember to keep the mass (m) and gravity (g) constant during your experiments.

a. What five values of k have you decided to test?

b. Go ahead and run your five experiments now. What period did you find for each value of k? c. In general, does a stiffer spring increase or decrease the period of the mass-spring system? Why do you think this is?

d. Explain the general relationship you found between the value of k and the period of the system. How is this relationship similar to the relationship between period and mass?

3. Now determine the effect that changing the acceleration due to gravity has on the period of the system. To do this, find the period for several values of g while holding m and k constant.

a. How does the motion of the spring change when g is increased? When g is decreased?

b. How is the value of g related to the period of the system? Explain your answer. Why do you think this is?

c. Suppose you could jump on a pogo stick for 15 seconds on the Moon. (Ignore the obvious complications.) Do you think you would complete more bounces, fewer bounces, or the same number of bounces as you can in 15 seconds on Earth? Explain.

4. Suppose the period of a given mass-spring system is 5 s. Explain two different ways you could change the period of that system to 1.25 s.