oscillatory motion l.
Skip this Video
Loading SlideShow in 5 Seconds..
Oscillatory Motion PowerPoint Presentation
Download Presentation
Oscillatory Motion

Loading in 2 Seconds...

play fullscreen
1 / 20

Oscillatory Motion - PowerPoint PPT Presentation

  • Uploaded on

Oscillatory Motion. Object attached to a spring Simple harmonic motion Energy of a simple harmonic oscillator Simple harmonic motion and circular motion The pendulum. An Object Attached to a Spring.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

Oscillatory Motion

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
oscillatory motion
Oscillatory Motion
  • Object attached to a spring
  • Simple harmonic motion
  • Energy of a simple harmonic oscillator
  • Simple harmonic motion and circular motion
  • The pendulum
an object attached to a spring
An Object Attached to a Spring

When acceleration is proportional to and in the opposite direction of the displacement from equilibrium, the object moves with Simple Harmonic Motion.

equation of motion
Equation of Motion

Second order differential equation for the motion of the block

The harmonic solution for the spring-block system


some terminology
Some Terminology

Angular frequency

Phase constant




properties of periodic functions

Angular Frequency






Properties of Periodic Functions
  • The function is periodic with T.
  • The maximum value is the amplitude.

f / w

properties of simple harmonic motion
Properties of Simple Harmonic Motion
  • Displacement, velocity and acceleration are sinusoidal with the same frequency.
  • The frequency and period of motion are independent of the amplitude.
  • Velocity is 90° out-of-phase with displacement.
  • Acceleration is proportional to displacement but in the opposite direction.
example p15 10
Example – P15.10
  • A piston in a gasoline engine is in simple harmonic motion. If the extremes of its position relative to its center point are 5.75 cm, find the maximum velocity and acceleration of the piston when the engine is running at the rate of 3750 rev/min.
the block spring system
The Block-Spring System

Frequency is only dependent on the mass of the object and the force constant of the spring

energy of the harmonic oscillator
Energy of the Harmonic Oscillator
  • Consider the block-spring system.
  • If there is no friction, total mechanical energy is conserved.
  • At any given time, this energy is the sum of the kinetic energy of the block and the elastic potential energy of the spring.
  • Their relative “share” of the total energy changes as the block moves back and forth.
example p15 18
Example – P15.18
  • A block-spring system oscillates with an amplitude of 3.70 cm. The spring constant is 250 N/m and the mass of the block is 0.700 kg.
    • Determine the mechanical energy of the system.
    • Determine the frequency of oscillation.
    • If the system starts oscillating at a point of maximum potential energy, when will it have maximum kinetic energy?
    • When is the next time it will have maximum potential energy?
the simple pendulum
The Simple Pendulum

The tangential component of the gravitational force is a restoring force

For small q (q < 10°):

The form as simple harmonic motion

damped oscillations
Damped Oscillations
  • Suppose a non-conservative force (friction, retarding force) acts upon the harmonic oscillator.
  • Restoring forces can result in oscillatory motion.
  • Displacement, velocity and acceleration all oscillate with the same frequency.
  • Energy of a harmonic oscillator will remain constant.
  • Simple harmonic motion is a projection of circular motion.
  • Resistive forces will dampen the oscillations.