1. Aim: How can we describe simple harmonic motion?
Do Now: Quiz
HW: Problem Set

2. If we stretch a spring to a point A, what is the force equivalent to?
F = -kx… Restoring F is opposite displacement.
This force is directly proportional to the displacement x the spring has been stretched.
k: spring constant or spring stiffness constant

3. Demo 1
If we place different masses with different weights on our spring, we can calculate the spring constant! How?
Graph F vs. x
Place 2 or 3 weights on the spring vertically and calculate the spring constant.
Then use probe ware and pull on spring to measure spring constant. They should be the same! Physics works!

4. Harmonic Motion
At A there will be a lot of PE, so upon being released where will there be the most KE? Why?
KE is max at x = 0 and then the block’s momentum keeps it traveling until it’s energy turns into PE again… E = .5mv2 + .5kx2

5. Graphing “x” as a function of time
x(t)
T is our period or time is takes to go from A to –A and back. (One full cycle)
At time T our block is also at A! A
If we start with spring extended out to A then we know that is the max the spring will be extended or compressed. The period is defined as one full cycle to come back to A when released, so we can plot many known points. Compressed at T/2 and on axis is equilibrium position. When we connect the points the line is curved because a straight line would insinuate constant speed and this object is accelerating. This is like a position time graph with acceleration.
T/2 T t -A
How do points connect?

6. Facts of Harmonic Motion
Simple Harmonic Motion (SHM): Any vibrating system for which the restoring force is directly proportional to the negative of the displacement.
Amplitude is the greatest distance from the equilibrium point.
Period: Time of one cycle
Frequency: Cycles per second (Hz)… f = 1/T

7. Pendulums Draw a FBD F = -mgSinθ Restoring force θ L F = -mgθ
For small angles θ
For a FBD: mg straight down and FT acting as tension up wire.
After FBD: mg breaks into components with mgCos opposite Tension and mgSin in direction of motion. m F

8. Period Equations (T) How are Springs and Pendulums related?
Both have harmonic motion, so both have a period (time of one oscillation).
Spring: T = 2π(m/k)1/2
Pendulum: T = 2π(L/g)1/2
Notice that these are similar, but based on slightly different variables!

9. Practice
A spider has a mass of .3 g and waits in its web of negligible mass. A slight movement causes the web to vibrate with a frequency of about 15 Hz. Estimate k for the web! At what frequency would you expect the web to vibrate if a bug of mass .1 g became trapped in addition to the spider?
Giancoli Textbook… pg. 293 Ch. 11

10. Practice
A geologist uses a simple pendulum that has a length of 37.1 cm and a frequency of Hz at a particular location on Earth. What is the acceleration due to gravity here?

11. Summary
Describe SHM
How does a stretched spring resemble energy conservation?
Define period, frequency and amplitude