Search
 
 

MATHEMATICS - CASE STUDY

    Introduction


Spring-mounted Slider
Click here to view movie (27 kB)

 

Chuck built a spring-mounted slider to illustrate simple harmonic motion to his son . He pushes the slider to the left side, releases it and the slider starts to move in the horizontal guide. He is curious about the velocity and acceleration 2 second after the slider starts moving.

What is known:

  • The displacement of the slider is expressed by
    s = 20 sin5t.
  • The time, t, is 2 seconds
     
    Questions

 

 

What is the velocity and acceleration of the slider 2 seconds after it starts to move?

     
    Approach


 
  • The first order derivative of the displacement with respect to time is velocity, ds/dt = v.
  • The second order derivative of the displacement with respect to time is acceleration, d2s/dt2 = a.
  • The first order derivative of velocity with respect to time is acceleration, dv/dt = a.