For this section we start with Hooke’s Law. But we already learned this. (partially)

In another chapter we learned That the Potential energy for A spring is PE = ½ mv 2 But Hooke’s Law is about the Force of a spring… F elastic = -kx

If a mass of 0.55 kg attached to A vertical spring stretches the Spring 2 cm from its equilibrium. What is the spring constant? k = 270 N/m

So a stretched or compressed Spring has elastic potential energy. A repeated motion, such as that Of a spring, is called periodic Motion. At the equilibrium position, velocity Reaches a maximum.

At maximum displacement, spring Force and acceleration is At its maximum. In simple harmonic motion, The restoring force is proportional To displacement. Simple harmonic motion is the Vibration about equilibrium Position in which a restoring Force is proportional to the Displacement from equilibrium.

A simple pendulum consists of A mass called a bob, which is Attached to a fixed spring.

The restoring force of a Pendulum is a component of The bob’s weight. So the forces acting on the bob At any point include the force Exerted by the string (y) and The bob’s weight resolved into Components in the y & x directions

For small angles, the pendulum’s Motion is simple harmonic. At any displacement, a simple Pendulum has gravitational Potential energy.

When measuring simple Harmonic motion, there are 3 major parts… Amplitude Period Frequency

Amplitude is the maximum Displacement from equilibrium. The period is the time it takes To execute a complete cycle. Frequency is the number of Cycles (or vibrations) Per unit time.

The SI unit for frequency is s -1, or hertz (Hz). There is a formula for this… f = 1T1T T = Period

The period of a simple pendulum Depends on string length And free-fall acceleration. T = 2π LgLg

What is the height if a pendulum If it has a period of 12s? L = 36m

You can do the same thing For a spring… The Period of a mass-spring System depends on mass And spring constant. T = 2π mkmk

The body of a 1275 kg car is Supported on a frame by four springs Each of which has a constant of 2 X people riding in the car Have a combined mass of 153 kg. Find the period of Vibration of the car when it is Driven over a pothole on the road? T = 0.84s

Transverse wave Compression Wave

A wave is the motion of A disturbance through a medium. A medium is the material through Which a disturbance travels. A mechanical wave is a wave Whose propagation requires The existence of a medium. A pulse wave is a single Non-periodic disturbance.

A periodic wave is a wave Whose source is some form Of periodic motion. Sine waves describe particles Vibrating with simple Harmonic motion. A transverse wave is a wave Whose particles vibrate Perpendicularly to the Direction of the wave motion.

And a longitudinal wave is a Wave whose particles Vibrate parallel to the Direction of wave motion. There are 4 terms used to Describe waves… Crest Trough Wavelength Speed

The crest is the highest point Above the equilibrium position. A trough is the lowest point Below the equilibrium position. The wavelength is the distance Between 2 adjacent similar Points of the wave. And speed is obviously how Fast the wave is moving.

A wave diagram

To find the speed of a wave Is found through a new formula. v = f λ v = velocity f = frequency λ = wavelength

The string of a piano vibrates With a frequency of 264 Hz. If the Sound has a wavelength of 1.3 m, what is the speed? v = 343 m/s

The law of superposition states That because waves are not Matter, but displacements of Matter, two waves can occupy The same space at the same time.

Although when waves Interact with each other, they may Be changed. Constructive interference is Interference in which individual Displacements on the same side Of the equilibrium position are Added together to form the Resultant wave.

Destructive interference is Interference in which individual Displacements on opposite Sides of the equilibrium Position are added together To form the resultant wave.

At a free boundary, waves Are reflected. At a fixed boundary, waves Are reflected and inverted. A standing wave is a wave Pattern that results when 2 waves Of the same frequency, Wavelength, and amplitude travel In opposite directions and interfere

A node is a point in a standing Wave that always undergoes Complete destructive Interference and therefore Is stationary. An antinode is a point on a Standing wave, halfway Between two nodes, at which The largest amplitude occurs.

The law of reflection states That the angle of incidence is Equal to the angel of reflection. Refraction is the change in Direction of waves at the Boundary of 2 different media. Diffraction is the spreading of Waves around the edge of a Barrier.

Law of Reflection Refraction