# A 0.45kg object attached to a hotizontal spring oscillates in simple harmonic motion with frequency 2Hz. If the object is released from rest at x=0.05m,find velocity and acceleration at x=0.05m,0.00,and -0.005m?

Aug 14, 2015

I am not sure it is easy to understand but have a look...

#### Explanation:

Have a look at the general idea:

In your case: Frequency: $\nu = 2 H z$, Period: $T = \frac{1}{\nu} = \frac{1}{2} = 0.5 s$ and $\omega = \frac{2 \pi}{T} = 2 \pi \cdot \nu = 2 \pi \cdot 2 = 4 \pi$ (initial fase is zero):

$x \left(t\right) = 0.05 \cos \left(4 \pi t\right)$

velocity:
$v = \frac{\mathrm{dx}}{\mathrm{dt}} = - 0.05 \cdot 4 \pi \sin \left(4 \pi t\right) = - 0.2 \sin \left(4 \pi t\right)$
$a = \frac{\mathrm{dv}}{\mathrm{dt}} = - 0.2 \cdot 4 \cos \left(4 \pi t\right) = - 0.8 \cos \left(4 \pi t\right)$

These can be plotted as (with time on the horizontal axis):

I also considered your displacements and times with the corresponding values of velocity and acceleration (the last time for $x = - 0.005 m$ is a little bit complicated...I had to improvise!).