lCalculating periods-1H l | Introduction: In activity A, you found that the period of a spring depends only on its mass and the spring constant. in activity B, you found that the period of a pendulum depends on its length and gravitational acceleration. Now. you will determine formulas for the period of each object. Question: How are the periods of pendulums and springs calculated? Summarize: Look at your results from prior activities. How did quadrupling m affect the period of the spring? How did quadrupling k affect the period of the spring? _ How did quadrupling L affect the period of the pendulum? How did quadrupling g affect the period of the pendulum? Gather data Use the Gizmo to find the period of the spring for three sets of m and kvalues. Then nd the period of the pendulum for three sets of f. and g values. Spring Pendulum Calculate: Calculate the ratios listed in the last three columns of each table. (Activity C continued on next page) Activity C (continued from previous page) m: Examine your data tables. No matter what values of m and kyou used for the spring, what is the ratio of the period to ? No matter what values of L and 9 you used for the pendulum, what is the ratio of the period to ? Challenge: Put together what you learned in this activity to come up with formulas for the period (1] of a spring based on its mass (m) and spring constant (k) and for the period of a pendulum based on its length (L) and gravitational acceleration (Q). Have your teacher check your formulas when they are complete. Apply: How long would a pendulum on Earth (where g = 9.8 m!52) have to be to have the same period as a spring with a mass of 10.0 kg and a spring constant of 25 Nlm