# Differential Calc

• Jun 13th 2006, 01:07 PM
mayster17
Differential Calc
The position ( in feet) of an object oscillating up and down at the end of a spring is given by s = A sin [ (square root of ( k/m)) * t ]
at time t ( in seconds). The value of A is the amplitude of the motion, k is a measure of the stiffness of the spring, and m is the mass of the object. Find the object's velocity at time t.
• Jun 13th 2006, 03:26 PM
Jameson
Velocity would be the derivative of position, so differentiate.

$\displaystyle v(t)=A\cos(\sqrt{\frac{k}{m}}t) \times \frac{d}{dx}\sqrt{\frac{k}{m}}t$

$\displaystyle v(t)=A\sqrt{\frac{k}{m}}\cos(\sqrt{\frac{k}{m}}t)$
• Jun 13th 2006, 04:36 PM
ThePerfectHacker
Quote:

Originally Posted by Jameson
Velocity would be the derivative of position

A slight error in terminology.
This was a distance/speed problem.

Problems with position/velocity based involved vector function and that is not the case here.
• Jun 13th 2006, 08:18 PM
CaptainBlack
Quote:

Originally Posted by ThePerfectHacker
A slight error in terminology.
This was a distance/speed problem.

Problems with position/velocity based involved vector function and that is not the case here.

Speed is intrinsicaly positive, here its velocity because it is signed
(that is a one dimensional vector).

RonL