2. Whenever the force acting on an object is: Whenever the force acting on an object is: 1. Proportional to the displacement 2. In the opposite direction, the object exhibits simple harmonic motion (SHM). the object exhibits simple harmonic motion (SHM). Examples Examples 1. mass attached to a spring 2. simple pendulum.

3. Definitions of Terms Definitions of Terms Amplitude = A = the maximum displacement of the moving object from its equilibrium position.Amplitude = A = the maximum displacement of the moving object from its equilibrium position. Period = T = the time it takes the object to complete one full cycle of motion.Period = T = the time it takes the object to complete one full cycle of motion. Frequency = f = the number of cycles or vibrations per unit of time.Frequency = f = the number of cycles or vibrations per unit of time.

4. Vertical Spring Mass Attached to a Spring m x = 0 “Equilibrium Position” x < 0 x > 0 x = displacement from equilibrium

5. Period of an object on a vertical spring exhibiting SHM is: T = period m = mass of object K = spring constant

6. Force always opposite the displacement from equilibrium  If we stretch a spring with a mass on the end and let it go, the mass will oscillate back and forth (if there is no friction).  This oscillation is called Simple Harmonic Motion, because F is a restoring force. Horizontal Spring

7. As previously stated, a simple harmonic oscillator is any object that oscillates and is subject to a restoring force. Example: horizontal mass on the end of a spring. F is a linear restoring force. Hooke’s law F= -kx applies F X

8. The frequency and period of the simple harmonic oscillator are independent of the amplitude.

9. t Sine or cosine curve representation of a restoring force and simple harmonic motion.

10. Another View

12. Case 2 - The Simple Pendulum. A component of the weight acts as the restoring force Component of weight restoring mass to equilibrium mg sin 

13. Period for The Simple Pendulum: A pendulum is made by suspending a mass m at the end of a string A pendulum is made by suspending a mass m at the end of a string of length L. The period of oscillation for small displacements is given by the following formula. T = period L = length “g”= acceleration due to gravity

15. Period of a simple harmonic oscillator representation in the form of a cosine curve. T/4 = time for quarter cycle T/2 = time for half cycle 3T/2 = time for three quarters of a cycle

16. Simple Harmonic Motion and Circular Motion, compared to circular motion

17. Energy in Simple Harmonic Motion

19. Mass-Spring System -- Example 1 Car hitting a pothole in the road.