Question

Define the following concepts and place them in a graph:

Amplitude (A)

Frequency (f)

Period (T)

Initial phase angle (?).

Answer 1

Consider a simple wave, that describes the motion of a system. Let us say the solution for that system is this,

This describes the value of x as it varies with time. If I were to take A = 5 and (strange values, I know but bear with me) and also and plot the graph,

Alright. We can already glean a lot of stuff from this plot. First, it looks like a wave. Then, the maximum value it seems to go to is 5. So, A = 5 seems to be the height of the wave from 0.

The maximum value that a periodic function achieves from its initial position is called the amplitude of the wave, A.

We can see that this function repeats itself. This means it is periodic in nature. But how do we see that? We can see that after t = 2, the function starts over as if it were back at t = 0. So, we can say that every t=2 units, the function repeats itself and hence its period is 2.

The time taken for a function to complete one full cycle is called the period of the fucntion T.

Alright. we know that frequency is the number of cycles per second, so,

The number of times a function completes a full cycle within a unit measure of time is called the frequency of a function, f.

f = 1/T

Now, we put which is nowhere to be seen in the graph. It is because it differently related,

This is called the angular frequency of a function.

Remember when we put = 0? Let's change that. Let me simultaneously draw a blue and red graph with different values of such that respectively.

By adding that extra value, what we essentially did was shift the t = 0 value or the initial value of the fucntion by . This value is called the phase angle and is given by, .