# Velocity and acceleration in SHM

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.

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

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Right. It looks like this:

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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?

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

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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?

```