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