Spring (simple harmonic motion) trig problems

Lessons

• 1.
  A mass is supported by a spring so that it rests 50 cm above a table top, as shown in the diagram below. The mass is pulled down to a height of 20 cm above the table top and released at time t = 0. It takes 0.8 seconds for the mass to reach a maximum height of 80 cm above the table top. As the mass moves up and down, its height h, in cm, above the table top, is approximated by a sinusoidal function of the elapsed time t, in seconds, for a short period of time.
  
  
  a)

  Graph how the height h of the mass varies with respect to the elapsed time t.
  
  
  b)

  Determine a sinusoidal function that gives the mass’s height h above the table top as a function of time t seconds
  
  
  c)

  What is the height of the mass 1.4 seconds after being released?
  
  
  d)

  Find the time t when the mass is 70cm above the table top for the third time?
  
  

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