Simple Harmonic Motion Given Amplitude and Frequency

  • #1

Homework Statement


A cheerleader waves her pom-pom in SHM with an amplitude of 17.3 cm and a frequency of 0.830 Hz .
Find the maximum magnitude of the velocity.


Homework Equations


v = -w Asin(ωt+Φ) = -wx
or
Conservation of Energy:
1/2kx2 + 1/2mv2 = 1/2kA2

The Attempt at a Solution


I tried v = -ω(x) using 0.173 as x
v = -5.21(0.173) = -0.0901 > wrong

I got the ω by solving for period T (1.205s), i then made this equal to 2π/ω to solve for omega.

I have yet to try the conservation of energy. But what would be the x in this case?
 

Answers and Replies

  • #2
I just realized that i had an extra 0 there for -0.0901, should have been 0.901!
 
  • #3
ehild
Homework Helper
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Homework Statement


A cheerleader waves her pom-pom in SHM with an amplitude of 17.3 cm and a frequency of 0.830 Hz .
Find the maximum magnitude of the velocity.


Homework Equations


v = -w Asin(ωt+Φ) = -wx
or
Conservation of Energy:
1/2kx2 + 1/2mv2 = 1/2kA2

The Attempt at a Solution


I tried v = -ω(x) using 0.173 as x
v = -5.21(0.173) = -0.0901 > wrong
There are to many 0-s. And the magnitude is not negative!
 
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  • #5
There are to many 0-s. And the magnitude is not negative!
I do have another question actually. How would i solve this?
"Find the speed when the pom-pom's coordinate is x= 9.40 cm ."

I tried to use the equation v = ωx and got 0. 48974, but i got the wrong answer
v = (5.21rad/s)(0.094m) = 0.4897
 
  • #6
ehild
Homework Helper
15,543
1,913
I do have another question actually. How would i solve this?
"Find the speed when the pom-pom's coordinate is x= 9.40 cm ."

I tried to use the equation v = ωx and got 0. 48974, but i got the wrong answer
v = (5.21rad/s)(0.094m) = 0.4897

The velocity is the time derivative of the displacement. If x=Acos(ωt) what is v=dx/dt?
V=ωA is the relation between maximum displacement and maximum speed.
 
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