Goal: to understand waves Objectives: 1)To learn about Oscillations and vibrations 2)To understand the properties of Waves 3)To learn about Transverse waves 4)To understand Interference 5)To learn about how to use waves scientifically

Pendulum One form of oscillation is a pendulum. You tie a mass to the end of a string. You pull that object up so that it has some potential energy. You let it go. What happens? Will the motion depend on the mass of the object on the string (assuming we can ignore the mass of the string)?

Period The time it takes the pendulum to do a full move back and forth is called the oscillation period. The period does NOT depend on mass! The period only depends on the length of the pendulum (assuming a small movement back and forth).

Period Equation T = 2 π * (L / g) 1/2 L is the length of the pendulum assuming that all the mass is at the end of the pendulum. Otherwise: T = 2 π * [I / (mgd)] 1/2

Example In the far future an astronaut explores a planet far away from Earth. To determine the surface gravity the astronaut uses a simple pendulum. The pendulum is 1.2 m long with a single mass of 2.3 kg at the end. The astronaut notices that the pendulum swings once every 2.4 seconds. What is the gravitational acceleration for the surface of this planet? NOTE: you will have a HW question similar to this.

A bit later The force the spring applies depends on the distance from the equilibrium point. The further away from that point the bigger the force. How will the magnitude of the force change with time? What about the direction?

Spring oscillations Otherwise known as Simple Harmonic Motions A spring that is pulled from equilibrium will return there. However, it will keep going as there is not yet a force to stop it. It will then go an equal distance to the other side. This will create an oscillation.

Frequency Frequency is how many times per second the oscillation occurs. That is f = 1 / T Frequency is in units of Hertz (1 Hertz = 1/s) Angular frequency is how long it takes to travel 1 rad of angle. w = 2 π * f

Skipping a long derivation You can thank me later For a spring w = (k/m) 1/2 Or T = 2 π * (m/k) 1/2 Let’s try a sample question: A 2 kg mass is attached to a spring with a spring coefficient of 20 N/m. The spring is compressed by 0.3 m. A) Find the angular frequency of the system B) Find the period of the system

Motions As the object moves back and forth the acceleration and velocity will change. Max a = w 2 Xmax = (k/m) Xmax Max v = w Xmax

Strain As an object is stretched it is strained. The amount of Strain is given by (assuming the stretching is a small fraction of the length): Strain = change in L / L

Example A bowling ball is placed on a foam cushion. Not sure why. The thickness of the cushion before the bowling ball is added is 0.25 m. If the bowling ball sinks 0.05 m into the cushion then what is the stress the bowling ball creates for the cushion?

Stress When forces are applied to a surface that is stress. Stress = F/A (yes this is pressure)

Example A car has a mass of 600 kg. The car has 4 tires with the weight spaced evenly over each tire. Each tire touches the ground over an area of 0.06 square meters. What is the stress that the tires put on the ground?

Hooke’s Law Stress and Strain are a ratio of each other. F/A = Y * (change in L / L) Y = Young’s Modulus Y is different for different materials. Y units are Pascals

Dog chain Instead of a chain a dog owner uses a metal cable to keep their large dog tied up. The dog’s maximum strength can exert is 450 N. The Young’s Modulus of Steal is 2 * Pa The cable will break if the strain exceeds A) What is the minimum area of cable needed? B) What is the minimum radius of cable needed?

Deformations When you press on an object it will compress. Some objects compress more than others. Foam compresses pretty easy. Metal, not so much F/A = S * (compression / L) S = the Shear Modulus

Conclusion We have learned about pendulums and spring oscillations We have examined stress and strain We have learned about Hooke’s Law