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13.1.3 Introduction to terms used

1.1.3 Introduction to terms used LO (c) 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]  Model:

  1. Run Sim

Suggested Activity Q1: run model with different starting x to explore the meaning of amplitude
Suggested Activity Q2: run model with different mass m and spring constant k to explore different period T, frequency f and angular frequency ω



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Software Requirements


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support full-screen? Yes. Chrome/Opera No. Firefox/ Samsung Internet Not yet Yes Yes
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cannot work on Internet Explorer 9 and below



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Video   Progressive mathematical modeling with OSP@SG by lookang lawrence wee






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