# Thread: Differential Calc

1. ## 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.

2. Velocity would be the derivative of position, so differentiate.

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

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

3. 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.

4. 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