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SHM20

1.6 Degrees of damping                    LO (i)


If no frictional forces act on an oscillator (e.g.  mass-spring system, simple pendulum system,  etc.), then it will oscillate indefinitely.
If no frictional forces act on an oscillator (e.g.  mass-spring system, simple pendulum system,  etc.), then it will oscillate indefinitely.
In practice, the amplitude of the oscillations decreases to zero as a result of friction. This type of motion is called damped harmonic motion. Often the friction arises from air resistance (external damping) or internal forces (internal damping).

1.6.1 if the motion is x= x0 sin(ωt), the following are the x vs t graphs for 2 periods, as an illustration of the damping.

when b=0.0 no damping, system oscillates forever without coming to rest. Amplitude and thus total energy is constant

1.6.1.1 No damping

when b=0.0 no damping, system oscillates forever without coming to rest. Amplitude and thus total energy is constant

when b=0.1 very lightly damp, system undergoes several oscillations of decreasing amplitude before coming to rest. Amplitude of oscillation decays exponentially with time.

1.6.1.2 Light damping

when b=0.1 very lightly damp, system undergoes several oscillations of decreasing amplitude before coming to rest. Amplitude of oscillation decays exponentially with time.

when b=2.0, critically damp system returns to equilibrium in the minimum time, without overshooting or oscillating about the equilibrium position amplitude.

1.6.1.3 Critical damping

when b=2.0, critically damp system returns to equilibrium in the minimum time, without overshooting or oscillating about the equilibrium position amplitude.

when b=5.0, very heavy damp, system returns to equilibrium very slowly without any oscillation

1.6.1.4 Heavy damping

when b=5.0, very heavy damp, system returns to equilibrium very slowly without any oscillation

1.6.2 a more typical starting position, is  x= x0 cos(ωt), the following are the x vs t graphs for 2 periods, as an illustration of the damping.





1.6.2.1 No damping

when b=0.0 no damping, system oscillates forever without coming to rest. Amplitude and thus total energy is constant


1.6.2.2 Light damping


when b=0.1 very light damping, system undergoes several oscillations of decreasing amplitude before coming to rest. Amplitude of oscillation decays exponentially with time.



1.6.2.3 Critical damping

when b=2.0 critically damp, system returns to equilibrium in the minimum time, without overshooting or oscillating about the equilibrium position amplitude.



1.6.2.4 Heavy damping

when b=5.0 very heavy damp,  system returns to equilibrium very slowly without any oscillation.

1.6.3 Model:

  1. Run Sim
  2. http://iwant2study.org/ospsg/index.php/84
 

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Software Requirements

SoftwareRequirements


Android iOS Windows MacOS
with best with Chrome Chrome Chrome Chrome
support full-screen? Yes. Chrome/Opera No. Firefox/ Samsung Internet Not yet Yes Yes
cannot work on some mobile browser that don't understand JavaScript such as.....
cannot work on Internet Explorer 9 and below

 

Credits

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http://iwant2study.org/lookangejss/02_newtonianmechanics_8oscillations/ejss_model_SHM20/SHM20_Simulation.xhtml

Apps

Cover arthttps://play.google.com/store/apps/details?id=com.ionicframework.shm20app163344&hl=en

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Parent Category: 02 Newtonian Mechanics
Category: 09 Oscillations
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