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Simple Harmonic Motion. Why is Acceleration proportional to NEGATIVE displacement?

  1. Jan 25, 2010 #1
    In Simple harmonic motion: Acceleration = -W^2 x (W being omega, rads per sec. and x beind displacement (distance if you will) ) Omega is a constant


    but why is acceleration proportional to the NEGATIVE displacement, in other words, why MINUS??

    Help appreciated. Thanks in advance!!
     
  2. jcsd
  3. Jan 25, 2010 #2
    Re: Simple Harmonic Motion. Why is Acceleration proportional to NEGATIVE displacement

    acceleration and displacement are vectors. they have direction. the acceleration is opposite in direction to the displacement and tries to bring it back. hence the minus sign to signify that the two vectors are opposite in direction.
     
  4. Jan 25, 2010 #3
    Re: Simple Harmonic Motion. Why is Acceleration proportional to NEGATIVE displacement

    yea baner is correct. This is why in simple harmonic motion we have sinusoidal functions representing the displacement velocity and acceleration.

    we know that the time derivative of displacement is velocity, and the time derivative of velocity is acceleration.

    so if we take the derivative of sine we get a cosine. then we take the derivative of a cosine and we get -sine. That -sine is representative of acceleration, and if you notice it is in the opposite direction of displacement.
     
  5. Jan 25, 2010 #4

    Doc Al

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    Staff: Mentor

    Re: Simple Harmonic Motion. Why is Acceleration proportional to NEGATIVE displacement

    To add to what banerjeerupak described, you might find it helpful to consider Hooke's force law (which leads to simple harmonic motion): F = -kx. The negative sign is important. When the displacement is positive, the restoring force (and thus the acceleration) is negative.
     
  6. Jan 25, 2010 #5
    Re: Simple Harmonic Motion. Why is Acceleration proportional to NEGATIVE displacement

    Because the spring is elastic, it resists a change in shape
     
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