Springs

• Hooke’s Law (Fs)

• Spring Constant (k)

• Spring Force – is a restoring force because it always pushes or pulls towards the equilibrium position.

kxFS

Simple Harmonic Motion

• Simple harmonic motion occurs when the net force along the direction of motion obeys Hooke’s Law – In other words, when the net force is

proportional to the displacement from the equilibrium point and is always directed towards the equilibrium point.

Fig. 15.3, p.456

Terminology

• Amplitude (A) – maximum displacement• Period (T) – time it takes the object to

move through one complete cycle• Frequency (f) – the number of complete

cycles per unit of time

• Acceleration (a)

xmka

kxFma

Tf 1

The Equations

Equations of Motionfor the object-spring system

Pendulum Equations

Types of Traveling Waves

• Transverse wave – the displacement of the wave is perpendicular to the motion of the wave– Sine and cosine graphs– Light waves (electromagnetic waves)

• Longitudinal wave – the displacement of the wave is parallel to the motion of the wave– Sound waves

Fig. 16.2, p.488

Fig. 16.5, p.489

Fig. 16.3, p.488

Fig. 16.10, p.495

Terminology and Equations

• Wavelength ()• Wave speed (v)

• Mass per unit length ()

• If the wave is traveling on a string then the wave velocity is defined as:

fT

v

Tv

lm

Fig. 16.8a, p.492

IMPORTANT

• There are two different velocities for a traveling transverse wave. – The wave speed, which is literally how fast

the wave is moving to the left or to the right.

– The transverse velocity, which is how fast the wave (rope, string) is moving up and down.

Wave Interference

• Superposition Principle – when two or more waves encounter each other while traveling through a medium, the resultant wave is found by adding together the displacements of the individual waves point by point.

Fig. 18.1, p.545

Fig. 18.2, p.546