# 5.21 Period of Simple Harmonic Oscillators

## Period of a simple pendulum

• A simple pendulum is:
• An object moving from side to side
• Attached to a fixed point above
• The time period of a simple pendulum can also be calculated using this equation:

= 2π • Where:
• l is the length of the pendulum swing
• is the strength of gravity on the planet on which the pendulum is set up

#### Worked example

A child is sitting on a swing that is 200 cm long. What is the period of oscillation?

Step 1: Convert length to meters

200 cm = 2 m

Step 2: Substitute the correct values

= 2π = 2π =2.84 s

The time period of 1 oscillation of the swing is 2.84 s

## Period of a Mass-Spring System

• A mass-spring system means:
• An object moving up and down
• On the end of a spring • The equation for the restoring force in SHM F = - kx
• is the same as the equation for Hooke's Law
• The time period, T can be calculated using the equation:

T = 2π • Where:
• m is the mass of the object on the end of the pendulum
• k is the spring constant of the material the pendulum is made from

#### Observing the Motion of a Mass-Spring System

• An experimental and graphical method can be used to observe the motion of a simple mass-spring system
• Tie a pencil together with the mass and set the mass in free oscillations by displacing it downwards slightly

• The oscillations will move the pencil up and down
• On a piece of graph paper, allow the pencil to trace the path of the oscillations by pulling the paper sideways as the mass-spring system oscillates up and down

• The oscillations will produce a curved, periodic graph
• This will decrease in amplitude as the mass-spring system slows down The motion of oscillator can be observed through a simple mass and spring system ### Get unlimited access

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