𝑥=3+2sin⁡(3𝑡)

The given equation is in the form of a sinusoidal function. Here, 'x' is the dependent variable and 't' is the independent variable. The equation represents a sinusoidal wave with a phase shift.

The general form of a sinusoidal function is: y = A sin(B(x - C)) + D

Where:

• A is the amplitude of the wave (the peak deviation of the function from zero).
• B is the frequency of the wave (how often the wave repeats).
• C is the phase shift (how far the function is shifted horizontally from the origin).
• D is the vertical shift (how far the function is shifted vertically from the origin).

In the given equation x = 3 + 2sin(3t),

• The amplitude of the wave is 2 (the coefficient of the sine function).
• The frequency of the wave is 3 (the coefficient of the variable 't').
• There is no phase shift as there is no constant being added or subtracted inside the sine function.
• The vertical shift is 3 (the constant being added to the sine function).

So, this equation represents a sine wave with an amplitude of 2, a frequency of 3, no phase shift, and a vertical shift of 3.