- #1
Wellesley
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Homework Statement
16. Suppose that a particle of mass 0.24 kg acted upon by a spring undergoes simple harmonic motion with the parameters given in Problem 1.
(a) What is the total energy of this motion?
(b) At what time is the kinetic energy zero? At what time is the potential energy zero?
(c) At what time is the kinetic energy equal to the potential energy?
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1. A particle moves back and forth along the x-axis between the points x = 0.20 m and x = –0.20 m. The period of the motion is 1.2 s, and it is simple harmonic. At the time t = 0, the particle is at x = 0 and its velocity is positive.
(a) What is the frequency of the motion? The angular frequency?
(b) What is the amplitude of the motion?
(c) What is the phase constant?
(d) At what time will the particle reach the point x = 0.20 m? At what time will it reach the point x = –0.10 m?
(e) What is the speed of the particle when it is at x = 0? What is the speed of the particle when it reaches the point x = – 0.10 m?
Homework Equations
f=frequency=0.83 Hz
[tex]\omega[/tex]= angular frequency= 2*pi*0.3= (5*pi)/3 or 5.23599 rad/s
T=period=1.2 s
m=mass=0.24 kg
A= amplitude=0.2 m
The Attempt at a Solution
My problem lies in part a of number 16: What is the total energy of this motion? The rest of the question I can solve easily.
I know the error has to do with the spring constant and the angular frequency.
[tex]\omega=[/tex][tex]\sqrt{k/m}[/tex]
k=[tex]\omega^{2}[/tex] * m
k=5.2359992*0.24=6.57974 N/m ----> [STRIKE]Pretty darn small for a spring constant.[/STRIKE]
I then tried this to make sure k was right:
T=2*pi*[tex]\sqrt{k/m}[/tex]
And got: k=6.57974 N/m
Then when I solve for total energy...
E=1/2kA2 -->1/2*6.57974 N/m *(0.2m)2--->E=.131595 J
The answer in the back is 6.6 Joules.
When I tried to work backwards, from the answer I get:
(6.6 J*2)/.22-->330 N/m as the spring constant.
I'm pretty sure my numbers are right...what could be throwing the answer off by a factor of fifty times? From past experience, I'm pretty certain the book isn't wrong, but in this case, I'm not sure...
Any help would be appreciated. Thanks!
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