Simple Harmonic Motion

Oscillatory Motion

Definition

Repetitive back-and-forth movement through a central, or equilibrium, position in which the

maximum displacement on one side is equal to the maximum displacement on the other.

Answers.com

http://www.answers.com/topic/simple-harmonic-motion-2

Motion that repeats in a simple patternMr. Dole

Period and Frequency

Period: Time needed to complete one cycle

Frequency: Number of cycles per second

Tf

1

Equation

Mass and Spring Pendulum

2m

Tk

2L

Tg

Problem #1

What is the period of a mass and spring system that consists of a 2 kg mass on a spring with a spring constant of 100 N/m?

22 2 0.89

100m

T sk

Problem #2

What is the period of a mass and spring system that consists of a 4 kg mass on a spring with a spring constant of 100 N/m?

42 2 1.26

100m

T sk

Problem #3

What is the period of a 5 m long pendulum on the earth?

52 2 4.49

9.8L

T sg

Problem #4

What is the period of a 5 m long pendulum on the moon (g=1.6 m/s2)?

52 2 11.1

1.6L

T sg

Problem #5A 5 kg mass is placed on a spring and set into motion. The period of the motion is 0.63 s. What is the spring constant of the spring?

2m

Tk

2 24m

Tk

224

497

mk

TNk m

Problem #6The frequency of a pendulum is measured to be 0.25 Hz. What is the length of the pendulum?

14T s

f

2L

Tg

2 24L

Tg

2

2 3.974

TL g m