1. Today’s Topic: Simple Harmonic Motion Explanation Learning Goal: SWBAT name the parts of a wave, and explain the relationship between frequency and period. Describe the similarities that exist between these two objects. Both are undergoing Simple Harmonic Motion!

2. Homework Complete the Pendulum Lab (Due Thursday, May 28 th ). Complete the Simple Harmonic Motion Worksheet. (Due Thursday, May 28 th )

3. Vibration All things around us are constantly wiggling and jiggling in place. However, most of these objects are too small to see. What are some objects that are currently wiggling and jiggling in this room?

4. Vibration Objects in their natural state of rest are in their equilibrium position. When objects move back and forth from their equilibrium position, they are said to be vibrating.

5. Vibration Vibrations need time in order to move back and forth, or oscillate. The pendulum we see up here, as well as the spring-mass system are examples of objects that move in simple harmonic motion. The true definition of simple harmonic motion is a bit unwieldy, but here it is:

6. Vibration Simple harmonic motion is a type of periodic motion where the force acting on the object is directly proportional to the displacement and acts in the direction opposite of displacement. Let’s pick this apart with the spring-mass. For all intents and purposes, think of the pendulum and spring-mass system here.

7. Period The time it takes for an oscillating object to complete one full cycle is its period. In Physics, period is written as T, and is measured in seconds. Think of T as the TIME it takes to complete one full oscillation.

8. Period of a Pendulum

9. Example Problem What is the period of a pendulum on Earth with a length of 70 cm? If this same pendulum were brought to Io, one of the moons of Jupiter where the acceleration due to gravity is 1.796 m/s 2, how much longer would the period be? Answer: 1.679 s Answer: 2.244 s

10. Period of a Pendulum Galileo Galilei was the first to observe and discover this fact – the mass of a pendulum has no effect on its period.

11. Period of a Pendulum MIT’s Walter Lewin demonstrated this discovery as well in one of his classes. Here, he compares the time it takes for 10 pendulum oscillations with and without extra mass.

12. More S.H.M. The mass and spring also exhibit simple harmonic motion. The period of the mass and spring system depends only on: The mass at the end of the spring The spring constant of the spring

13. More S.H.M.

14. Example Problem A mass-spring system oscillates with a period of 0.45 seconds. What is the spring constant of the spring if the mass is 625 grams? Answer: 121.847 N/m

15. Period and Its Inverse A 6.2 cm long pendulum oscillates very quickly. What is the period of this pendulum? So how many seconds does it take per swing? What if we wanted to know how many swings it can make per second? Answer: 0.5 s

16. Period and Its Inverse Flip that upside-down! The period tells us how many seconds it takes for one complete cycle to occur. If we wanted to know how many cycles occur in one second, we would be asking for its frequency.

17. Frequency [Hz] [s] 1 fT

18. Frequency The units for frequency are the Hertz. They are named after the German scientist Heinrich Hertz – who did extensive work in the field of electromagnetism, as well as radio transmission. He was the first to conclusively prove the existence of electromagnetic waves.

19. Frequency