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SHM11

1.2.5 Example

The graphs show how the variation with time of the velocity, v and the acceleration, a of a body when it is oscillating with simple harmonic motion.
(a)    Determine the period, T.
(b)    Sketch the variation with time of the displacement, x, of the oscillating body
[ 2.09 s, x = 2  sin( 3t )]

1.2.5.1 Solution:

a) maximum velocity , v0 = x0ω = 6 m/s

maximum acceleration a0 = x0ω2 = 18 m/s2

thus dividing the 2 equations, we get ω = 3 rad/s

therefore since ω = 2 π T

3 = 2 π T

T = 2 π 3

T = 2.09 s

b) since maximum velocity , v0 = x0ω = 6 m/s and we now know ω = 3 rad/s earlier

x0(3) = 6

x0 = 2 m

using the model to test check out your answer!


1.2.5.2 Model:

  1. Run Sim
  2. http://iwant2study.org/ospsg/index.php/73
 

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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

 

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