Measuring Simple Harmonic Motion

Chapter 12 Section 2

Measuring The Motion There are 3 things that determine the motion

of a mass in simple harmonic motion. Amplitude Period Frequency

Amplitude Amplitude – The maximum displacement

from the equilibrium position. Can be measured in different ways

Pendulum – The angle (radians) between the equilibrium position and the maximum displacement.

Spring-mass – The maximum amount (meters) stretched or compressed from the equilibrium position.

Period Period – The time it takes to execute a

complete cycle of motion. For example:

If it takes 5 seconds for a person on a swing to swing back and forth, then the period of the motion would be 5 seconds.

SI units for period – Seconds (s) Variable given for period – Capital letter (T)

Displacement For Period The displacement of an object in simple

harmonic motion during the time of 1T (time to compete one cycle) is “ZERO.”

Frequency Frequency – The number of cycles or

vibrations per unit time. For example:

The person on the swing completes one cycle in 5 seconds, the frequency would be 1/5 cycles per second or 0.2 cycles per second.

Units For Frequency SI units for frequency – S-1

This is known as Hertz (Hz) Variable for frequency – lower case letter (f) In the case of the person swinging, the

frequency would be: 0.2 cycles per second = 0.2 Hz

A typical TV set has a frequency of 60Hz, which means 60 frames per second.

Differences Between Period and Frequency Period is time per cycle. Frequency is the number of cycles per unit

time. They are inversely proportional.

Equations For Frequency and Period

If the period or the frequency is known, this relationship can be used to calculate the other value. Period (s) Frequency (Hz)

Determining The Period of a Pendulum The strings length and the free fall

acceleration determine the period of a simple pendulum.

Things that don’t determine the Period: Amplitude (for angles less then 15 degrees) Mass of the bob

Simple Pendulum Equation

Example Problem #1 A desktop toy swings back and forth once

every 1.0 seconds. How tall is this toy?

Example Problem #1 Answer length = 0.25m

Example Problem #2 What is the period of a 3.98m long

pendulum?

Example Problem #2 Answer T = 4.00 seconds

Period of a Mass-Spring System The mass attached to the spring and the

spring constant (k) determine the period. Things that don’t determine the period:

Amplitude

Period of a Mass-Spring System Equation

Example Problem #3 A 1.0 kg mass attached to one end of a

spring completes one oscillation every 2.0 seconds. Find the spring constant.

Example Problem #3 Answer k = 9.9N/m