Peoples Physics Concepts

http://www.ck12.org Chapter 10. Simple Harmonic Motion

10.1 Harmonic Period and Frequency

• Describe the concepts of period and frequency.


• Read the period and frequency off a graph and calculate them for systems in harmonic motion.

Students will learn the concepts of period and frequency and how to read them off a graph and how to calculate

them for systems in harmonic motion. In addition, students will learn how to graph simple harmonic motion.

Key Equations

Period Equations















T=^1 f Period is the inverse of frequency

Tspring= 2 π

√

m

k

Period of massmon a spring with constantk

Tpendulum= 2 π

√

L

g

Period of a pendulum of lengthL

Kinematics of SHM

{

x(t) =x 0 +Acos 2πf(t−t 0 ) Position of an object in SHM of AmplitudeA

v(t) =− 2 πf Acos 2πf(t−t 0 ) Velocity of an object in SHM of AmplitudeA

Guidance

Example 1

A bee flaps its wings at a rate of approximately 190 Hz. How long does it take for a bee to flap its wings once

(down and up)?

Question: T=? [sec]

Given: f= 190 Hz

Equation: T=^1 f

Plug n’ Chug: T=^1 f= 1901 Hz= 0. 00526 s= 5. 26 ms

Answer:

5 .26 ms

Example 2

Question: The effectivekof a diving board is 800N/m (we say effective because it bends in the direction of

motion instead of stretching like a spring, but otherwise behaves the same). A pudgy diver is bouncing up and

down at the end of the diving board. The y vs. t graph is shown below.

a) What is the distance between the lowest and the highest point of oscillation?

b) What is the Period and frequency of the diver?

c) What is the diver’s mass?

d) Write the sinusoidal equation of motion for the diver.