# SHM find F, with A, v, and m

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..