Simple Harmonic Motion (SHM)

Mass on a Spring Periodic Motion – any repeated motion. pendulum

Mass on a Spring Equilibrium Position F = 0, a = 0, v = max Compressed Notice: F always points towards equilibrium (x=0). This is called a restoring force. Compressed F = max, a = max, v = 0 If there were friction, the mass would slow down and stop. This is called damping. Stretched F = max, a = max, v = 0

Hooke’s Law http://phet.colorado.edu/en/simulation/mass-spring-lab Force is proportional to displacement SHM occurs whenever the restoring force is proportional to displacement k = spring constant (N/m) measures the stiffness of the spring x = displacement from equilibrium (m) When might we want damped oscillations?

1. If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?

2. Suppose the spring in problem #1 is replaced with a spring that stretches 36cm from its equilibrium position. What is the new spring’s spring constant? Is the spring stiffer or less stiff than the spring in problem #1?

Pendulums Amplitude (A) = max displacement from equilibrium Period (T) = time to complete one cycle of motion (back and forth) measured in seconds Frequency (f) = number of cycles per second (Hertz – Hz)

Pendulums Period (T) depends on Length of string (L) http://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html Period (T) depends on Length of string (L) acceleration due to gravity (g) Notice: T does not depend on m or A

Mass on a Spring Period (T) depends on mass (m) spring constant (k) http://phet.colorado.edu/en/simulation/mass-spring-lab Period (T) depends on mass (m) spring constant (k) Notice: T does not depend on A

Energy of SHM

9. a) You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and its period is 12 s. How tall is the tower?

Wave Motion A wave is the movement of a disturbance through a medium A medium is the material the wave travels through - mechanical waves require a medium - electromagnetic waves do not require a medium http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html

Wave Types Pulse Periodic Sine Transverse Longitudinal http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html Pulse Periodic Sine Transverse Longitudinal

Transverse Wave

Longitudinal Wave

Waves Energy of a wave is proportional to A2 Wave Speed (v) depends on the medium Wave Frequency (f) depends on the source # of crests passing each second

Superposition & Interference

Superposition & Interference

Reflection http://phet.colorado.edu/en/simulation/wave-on-a-string

Interference Pattern

Standing Waves

Standing Waves

Standing Waves Harmonic Series: