A block hanging down from a spring has a mass of 5 kg. The spring stiffness constant is 1000 N/m.

The block was displaced from the equilibrium state by 10 cm and released.

Find the amplitude, period, and angular frequency.

Determine the velocity and acceleration of the block at 5 cm distance from the equilibrium position.

**Solution:**

The amplitude of the block is the maximum distance that the block travels from its equilibrium state:

A=10 cm=0.1 m

The angular frequency can be found from the following equation:

To find the period we need to find the frequency first:

Now the period can be determined:

It is known that the velocity is the first order derivative of the displacement function:

The acceleration is the first order derivative of the velocity function:

The displacement function can be written as:

Knowing the distance, we can find the time at which the block will be at that point:

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