13.1.3      Introduction to terms used LO (c)

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 _ B O P A  

instantaneous position _ B O P A  

maximum amplitude _ B O P A m

minimum amplitude _ B O P A m

Given the equation x = x₀ sin ( ω t ) can describe SHM, suggests the usual symbols associated to the physical quantity

central equilibrium position  _ 0 x x0 -x0 w t T f  

instantaneous position or displacement given by vector OP  _ 0 x x0 -x0 w t T f m

maximum amplitude  _ 0 x x0 -x0 w t T f m

minimum amplitude  _ 0 x x0 -x0 w t T f m

time taken for one complete oscillation, for example Path from O→A→O→B→O   _ 0 x x0 -x0 w t T f s

number of oscillations performed per unit time _ 0 x x0 -x0 w t T f 1/s. Hence, f and T are related by the equation ${\displaystyle f=\frac{1}{T}}$

angular frequency _ 0 x x0 -x0 w t T f   rad/s. Since one complete oscillation is 2π radians, ω and f are related by ω = 2π f
 
 

Example 4 

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_SHMxvavertical01/SHMxvavertical01_Simulation.html
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