1. Simple Harmonic Motion Physics Ms. Shaver

3. Periodic Motion

4. Simple Harmonic Motion: 1.Is a periodic motion that repeats at constant frequency. 2.Has a restoring force that acts to restore the oscillator to equilibrium. F=-kx Hooke’s Law x: displacement from equilibrium k: spring constant

5. Characteristic Quantities of Simple Harmonic Motion Displacement: distance from equilibrium. Amplitude: maximum displacement

6. Characteristic Quantities of Simple Harmonic Motion Frequency: oscillations per unit time –Unit: 1/sec =Hertz Period: time to complete one oscillation –Unit: sec f=1/T T=1/f

7. Simple Harmonic Motion Velocity: –maximum as it passes through equilibrium –zero as it passes through the extreme positions in its oscillation. Acceleration: a=F/m = -kx/m -maximum at extreme points -zero at equilibrium

8. Mass on a Spring Applet: http://www.walter-fendt.de/ph14e/springpendulum.htm

9. Position vs Time Graph of Mass on Spring (Sine Curve) a)What is the amplitude? b)What is the period? c) What total distance does the particle travel in one period? x

10. Period of A Spring Mass Oscillator ____ T=2  √m/k T period (s) m mass (kg) k spring constant (N/m)

11. Problem Calculate the period of a mass of 5kg on a spring that has a spring constant of 20N/m. Answer: 3s

12. Question If you had a spring-mass system on the moon, would the period be the same or different than that of this system on the earth? NO. mass and spring constant do not depend on gravity.

13. Solve for m or k

14. Harmonic Motion of a Pendulum Applets: http://www.walter-fendt.de/ph14e/pendulum.htm http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulati ons6e/index.htm?newwindow=true http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulati ons6e/index.htm?newwindow=true L

15. Harmonic Motion of a Pendulum http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulati ons6e/index.htm?newwindow=truehttp://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulati ons6e/index.htm?newwindow=true Period ___ T=2  √L/g g=9.8m/s 2 L=length of string L

16. Problem Calculate the Period of a pendulum of length 0.75 m. Answer: 1.7s

17. Question If you had a pendulum on the moon would its period be the same or different compared to the same pendulum on the earth? Different because the period depends on gravity, which on the moon is 1.62 m/s 2

18. Solving for g or L

19. Questions Does the period of a pendulum depend on the mass of the bob? If you increase the length of the pendulum string, what happens to the period? NO. There is no m in the equation. It will increase by the square root of L.

20. Calculating k from a F vs x Graph k is the slope of a F vs x graph Slope = rise/run = 100 N/5 m = 20 N/m F = -kx Y = mx + b