Mass oscillating on spring

  • Thread starter veitch
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  • #1
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Homework Statement



The position of a mass that is oscillating on a spring is given by x(t) = (14.5cm)cos[(14.0s-1)t].
What is the speed of the mass when t = 0.820 s?

Homework Equations



A= Amplitude
W= Angular frequency

x(t) = ACos(Wt)
v(t) = -WASin(Wt)

The Attempt at a Solution



v(0.820) = (-14.0)(14.5)Sin[(14.0)(0.820)]
= (-203)Sin[11.48]
= -40.4 cm/s

This seems so easy and yet apparently I have the wrong answer... any insight? :/ Thanks in advance
 

Answers and Replies

  • #2
fluidistic
Gold Member
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What you did seems right to me.
 
  • #3
122
1
Check the units of your frequency. It looks like you have the value in Hertz (or oscillations per second); try converting the instances of frequency to radians per second (and if you're carrying out the sine calculation on a calculator then change the mode to radians instead of degrees).
 
  • #4
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Check the units of your frequency. It looks like you have the value in Hertz (or oscillations per second); try converting the instances of frequency to radians per second (and if you're carrying out the sine calculation on a calculator then change the mode to radians instead of degrees).
Okay, that makes more sense...

W=2 x pi x freq

thus v(t) = -(2 pi 14)(14.5)Sin[(2 pi 14)(0.82)]

which gives -160 cm/s (with 3 sig figs)... but it still isn't right.
I suppose there shouldn't be a negative should there? Since speed is scalar... but 160 isn't the right answer either. :/
 

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