- #1
Yubsicle
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Homework Statement
A simple harmonic oscillator, with oscillations in the x direction, has velocity given by: $$v_{x} = (2.2 \frac {\mathrm{m}} {\mathrm{s}}) \sin [(6.9 \frac {\mathrm{rad}} {\mathrm{s}}) t]$$.
Find the values of ##\omega , A, f , T ,## and ##\phi##
Homework Equations
$$v_{x} = \frac {dx}{dt}$$
$$x = A \cos (\omega t - \frac{\pi}{2}) = A \sin \omega t$$
$$\omega = \frac{2\pi}{T} = 2 \pi f$$
The Attempt at a Solution
I integrated v with respect to t and got $$x = (-0.3188\mathrm{m})\cos [(6.9\frac{rad}{s} t)] $$
(I'm assuming that the integration constant C = 0, please correct me if I'm wrong). The first problem I have is that A is negative, and my understanding is that amplitude can only be positive. Do I take the absolute value of -0.3188 and get ##A = 0.3188##, did I make a mistake, or do I need to do more steps?
The second problem is that the formula is ##x = A \cos (\omega t - \frac{\pi}{2})## but i don't have a ##-\frac{\pi}{2}## anywhere. Again, is there an easy fix, did I mess up, or have I not completed all the steps needed? Thanks in advance.