Period of Oscillation Equation Sample

period of oscillation equation

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:

period of oscillation equation sample
To find the period we need to find the frequency first:

period of oscillation equation example

Now the period can be determined:

angular frequency of oscillation formula

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

angular frequency of oscillation formula example

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

The displacement function can be written as:

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

amplitude of oscillation equation example

If you study physics, then this sample period of oscillation equation will help you. We hope that it is understandable and clear to you. There are different types of samples that you can find on our blog. You will perform better if you use them, as they contain useful ideas.

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