Tuesday, January 13, 2015

SHM Chapter 04 SHM terms

Introduction to terms used LO (c)


https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM04/SHM04_Simulation.xhtml

Run Model

https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxva/SHMxva_Simulation.html

Q1: Consider an object P oscillating between point A and B about the origin (0,0), assuming the usual Cartesian Coordinate System apply.  Observe the Model and suggests possible meaning of the following points with the most suitable descriptions.
central equilibrium position  
instantaneous position  
maximum amplitude m
minimum amplitude m
Given the equation x = x0 sin ( ω t ) can describe SHM, suggests the usual symbols associated to the physical quantity
central equilibrium position   
instantaneous position or displacement given by vector OP  m
maximum amplitude  m
minimum amplitude  m
time taken for one complete oscillation, for example Path from O→A→O→B→O   s
number of oscillations performed per unit time 1/s. Hence, f and T are related by the equation  f = 1 T
angular frequency rad/s. Since one complete oscillation is 2π radians, ω and f are related by ω = 2π f


Example


The displacement of a spring mass system from a fixed point is as shown. From the graph, determine the
(a)     amplitude,      
(b)     period,     
(c)     frequency,      
(d)     angular frequency, of the oscillations.
[2.00 m, 6.28 s, 0.159 Hz, 1.00 rad s–1]

Run Model:


https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM04/SHM04_Simulation.xhtml
Q1: run model with different starting y to explore the meaning of amplitude
Q2: run model with different mass m and spring constant k to explore different period T, frequency f and angular frequency ω