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Oscillations - Finding Displacement at a Speed, Given Displacement at Another Speed

  • Thread starter Glorzifen
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  • #1
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Homework Statement


A 0.10kg mass is on a spring with k = 0.10 N/m. At time t=0s it crosses x=0m with a velocity of 2.0m/s. What is its displacement when v=1.0m/s?

Homework Equations


x(t) = Acos(wt + [tex]\varphi[/tex])
v(t) = -wAsin(wt + [tex]\varphi[/tex])
w = [tex]\sqrt{k/m}[/tex]

The Attempt at a Solution


According to the question...shouldn't v(0) = 2? When a plug those numbers into the v(t) equation I get: v(0) = -wAsin(0) = 0...in other words, v(0) = 0...what am I missing here? I have an idea of where to go from here, but if someone could clarify how I'm supposed to start, that would be great. Thanks for your time.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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The Attempt at a Solution


According to the question...shouldn't v(0) = 2? When a plug those numbers into the v(t) equation I get: v(0) = -wAsin(0) = 0...in other words, v(0) = 0...what am I missing here? I have an idea of where to go from here, but if someone could clarify how I'm supposed to start, that would be great. Thanks for your time.
Remember you have x=Acos(ωt+φ) so x(0) = Acosφ

v=Aωsin(ωt+φ), v(0) does not give you Aωsin(0), remember there is still φ which is unaffected by t being equal to zero.
 
  • #3
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Remember you have x=Acos(ωt+φ) so x(0) = Acosφ

v=Aωsin(ωt+φ), v(0) does not give you Aωsin(0), remember there is still φ which is unaffected by t being equal to zero.
Okay - not sure if this route even needs to be undertaken at all though...does this work?:

Etotal = [tex]\frac{1}{2}[/tex]kx2 + [tex]\frac{1}{2}[/tex]mv2

Etotal = 0 + [tex]\frac{1}{2}[/tex]0.1(2)2

Etotal = 0.2

0.2 = [tex]\frac{1}{2}[/tex](0.1)x2 + [tex]\frac{1}{2}[/tex]0.1(1)2

x = 1.7

Does that work?
 
  • #4
rock.freak667
Homework Helper
6,230
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Yes that works just as well.
 

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