Simple Harmonic Motion

Simple Harmonic Motion

Periodic Motion- repeated motion that occurs back and forth over same path.

Simple Harmonic Motion- If the force that restores the object back to its

equilibrium position is directly proportional to the displacement of the object.

- Described by AMPLITUDE, PERIOD and FREQUENCY.

SHM

AMPLITUDE (A)-magnitude of the maximum displacement or the maximum distance of a mass or particle from its equilibrium position.

PERIOD (T)- the time needed to repeat one complete cycle of motion.

FREQUENCY (f)- the number of cycles per second. A cycle is a complete round trip or motion through a complete oscillation.

Period and frequency are reciprocals of each other.

T=1/ff=1/T

Sample Problem

What is the period of a spring that is oscillating in a frequency of 27.1Hz.?

T=1/fT=1/27.1HzT=0.04/s

Hooke’s Law

F=-kxF=forcek=spring constantx=displacement

Sample Problem

A jack-in-the-box lid will pop open when a crank is turned on the outside of the box. If Jack pushes inside of the box with a force of 2.5N when the lid is closed and the spring is compressed 10.0cm from equilibrium, what is the force constant of the spring?

Given: Find: kFelastic=2.5Nx=10.0cm=0.1m

Solution:F=-kxk=-F/xk=-2.5N/0.1mk=-25.0N/m

Exercises

1. What is the frequency of the ball bouncing 0.23/s, assuming that it bounces in a vacuum?

2. The spring is hanging on the wall and a kid put a mass on it, what is the force constant as the force inserted is 1.72N and the string

were stretched at 25cm.

Assignment:

Juliet is on a swing that hangs from a tree branch by 2.0 m long ropes. What frequency will Juliet have as she swings?

Simple Pendulum

T= period of the pendulumL=length of the stringG=acceleration due to gravity

Sample Problem

Juliet is on swing that hangs from a tree branch by 2.0-m long ropes. What frequency will Juliet have as she swings?

Sample Problem

What is the frequency of an acrobat swinging on a trapeze if the cables are approximately 1.5m long?

Exercises:

An acrobat swings from a trapeze with a frequency of 0.25Hz. What is the length of the trapeze cable?