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SHM find F, with A, v, and m

  • Thread starter izzyfish
  • Start date
  • #1
1
0
I feel like an idiot for not being able to answer this question, it seemed so simple yet so complicated in my head.

Homework Statement


Have to find frequency, given the amplitude, velocity, and mass.
I don't have numbers as it was off an exam I just took. Guessing it was v=5 m/s; A=10m; and m=3kg.


Homework Equations


I was thinking of taking the derivative of the SHM eq x(t) = Asin(wt) but then I wasn't sure if I could calculate the spring constant with F = -K(xo - xf).


The Attempt at a Solution


My attempt was guessing, but if we threw in numbers, A=10m, v=5m/s, m=3kg...
x(t) = A * sin(wt)
w = 2 * PI * f
x(t) = A * sin(2 * PI * f * t)
v(t) = 2 * PI * f * A * cos(2 * PI * f * t)
t = 0
5 = 2 * PI * f * 10 * cos(2 * PI * f * 0)
5 = 2 * PI * f * 10 * 1
5 = 20 * PI * f
5 / (20 * PI) = f
f = 0.0795Hz

or..

F=-K(x-xo)
F = 3*9.8 = 29.4
x = 10
xo = 0
K = 2.94 N/m
f = (1 /( 2 * PI )) * sqrt( k / m)
f = 0.159 * sqrt (2.94 / 3 )
f = 0.1576 Hz

Would love to know the correct way to do this, as I'm confused..
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
Using F=kx would depend on how the spring is orientated. But I would use your first method.
 

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