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Periodic Motion (Springs and Pendulums)

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Title: PowerPoint Presentation Author: Mark Hossler Last modified by: Mark Hossler Created Date: 4/28/2010 6:00:07 PM Document presentation format – PowerPoint PPT presentation

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Title: Periodic Motion (Springs and Pendulums)


1
Periodic Motion(Springs and Pendulums)
  • January 4, 2015

2
Periodic Motion
  • Motion that repeats itself over a fixed and
    reproducible period of time is called periodic
    motion.
  • The revolution of a planet about its sun is an
    example of periodic motion. The highly
    reproducible period (T) of a planet is also
    called its year.
  • Mechanical devices on earth can be designed to
    have periodic motion. These devices are useful
    timers. They are called oscillators.

3
Simple Harmonic Motion
  • You attach a weight to a spring, stretch the
    spring past its equilibrium point and release it.
    The weight bobs up and down with a reproducible
    period, T.
  • Plot position vs time to get a graph that
    resembles a sine or cosine function. The graph is
    sinusoidal, so the motion is referred to as
    simple harmonic motion.
  • Springs and pendulums undergo simple harmonic
    motion and are referred to as simple harmonic
    oscillators.

4
Analysis of graph
Equilibrium is where velocity is maximum
3
t(s)
2
4
6
-3
x(m)
5
Analysis of graph
3
t(s)
2
4
6
-3
Maximum and minimum positions have velocity of
zero.
x(m)
6
Oscillator Definitions
  • Amplitude
  • Maximum displacement from equilibrium.
  • Period
  • Length of time required for one oscillation.
  • Frequency
  • Number of oscillations per second
  • f 1/T
  • Unit Hz or s-1

7
Demo
  • Determine the amplitude, period, and frequency of
    an oscillating spring using the motion sensors.
    See how this varies with the force constant of
    the spring and the mass attached to the spring.

8
Springs and Pendulums
  • January 4, 2015

9
Springs
  • Springs are a common type of simple harmonic
    oscillator.
  • Our springs are ideal springs, which means
  • They are massless.
  • They are both compressible and extensible.
  • They will follow Hookes Law.
  • F -kx

10
Hookes Law
Fs -kx
  • The force constant of a spring can be determined
    by attaching a weight and seeing how far it
    stretches.

11
Period of a spring
  • T period (s)
  • m mass (kg)
  • k force constant (N/m)

12
Sample Problem
  • Calculate the period of a 300-g mass attached to
    an ideal spring with a force constant of 25 N/m.

13
Sample Problem
  • A 300-g mass attached to a spring undergoes
    simple harmonic motion with a frequency of 25 Hz.
    What is the force constant of the spring?

14
Sample Problem
  • An 80-g mass attached to a spring hung vertically
    causes it to stretch 30 cm from its unstretched
    position. If the mass is set into oscillation on
    the end of the spring, what will be the period?

15
Spring combinations
  • Parallel combination springs work together.
  • Series combination springs work independently

16
Question?
  • Does this combination act as parallel or series?

17
Pendulum Lab
  • Do it before moving on.

18
Pendulums
  • The pendulum can be thought of as a simple
    harmonic oscillator.
  • The displacement needs to be small for it to work
    properly.

19
Pendulum Forces
20
Period of a pendulum
  • T period (s)
  • l length of string (m)
  • g gravitational acceleration (m/s2)

21
Sample problem
  • Predict the period of a pendulum consisting of a
    500 gram mass attached to a 2.5-m long string.

22
Sample problem
  • Suppose you notice that a 5-kg weight tied to a
    string swings back and forth 5 times in 20
    seconds. How long is the string?

23
Sample problem
  • The period of a pendulum is observed to be T.
    Suppose you want to make the period 2T. What do
    you do to the pendulum?
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