Suppose that a block of mass **M = 2 kg **
hangs from a spring of force constant **k = 20 N/m**.
The block is at rest, motionless.

You then raise the block a distance **y = 0.1 m**
vertically, and release it.
The block starts to bob up and down, up and down.

Q: Can you write an equation which describes thepositionof the block as a function of time?

Right. It looks like this:

Q: In this particular case, what is the value of the amplitude A? Q: In this particular case, what is the value of the angular frequency ω?

But that only tells us the **position** of the block.
What if we want to know how fast the block is moving
at any time -- the **velocity** of the block?

Q: Is there some way to write down the velocity as a simple function of time?

Indeed there is: take the derivative of position with respect to time.

Q: In this particular case, what is the maximum speed of the block?

In a similar manner, we can compute the acceleration of the block at any time by taking the time derivative of the velocity:

Q: In this particular case, what is the maximum acceleration of the block?

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.