Position in Motion: When to Use Cos & Sin in x=A*sin(wt+phi) or x=A*cos(wt+phi)?

[Tricks67]

In what kind of cases do u we formulate the equation type x=Asin(wt+phi) or x=Acos(wt+phi)...and if for example we use it to define the position of some thing in motion when do we know when to use cos and when to use sin...?

 

[AlephZero]

It doesn't really matter which you use. The only difference is what position on the wave corresponds to phi = 0. A sin(wt+phi + pi/2) = A cos(wt+phi)

 

[jtbell]

when do we know when to use cos and when to use sin...?

It depends on the initial conditions for your specific situation. If the object is at x = 0 when t = 0, then it's easiest to use a sine wave. If the object is at x = maximum (i.e. the amplitude) when t = 0 then it's easiest to use a cosine wave.

However, as AlephZero noted, you can use either kind of wave in any case, by including an appropriate phase factor.

 

[Tricks67]

and we find the phase factor by setting x=0, right?

 

[PJC01]

The equation x=A*sin(wt+phi) or x=A*cos(wt+phi) is known as a sinusoidal function, and it is commonly used to describe the position of an object in motion. The variable x represents the position of the object at a given time, t represents time, A is the amplitude of the motion, w is the angular frequency, and phi is the phase shift.

In general, both sine and cosine functions can be used to describe the position of an object in motion. The choice between using sine or cosine depends on the starting position of the object and the direction of its motion. If the object starts at its maximum position and moves in a clockwise direction, then the cosine function should be used. On the other hand, if the object starts at its maximum position and moves in a counterclockwise direction, then the sine function should be used.

It is important to note that both sine and cosine functions have the same shape but are shifted by a phase difference of pi/2. This means that they have the same amplitude and frequency, but their peaks and valleys occur at different times. Therefore, it is crucial to determine the starting position and direction of motion of the object in order to correctly choose between sine and cosine functions.

In summary, the choice between using sine or cosine in the equation x=A*sin(wt+phi) or x=A*cos(wt+phi) depends on the starting position and direction of motion of the object. It is important to carefully analyze the situation and determine these factors in order to accurately describe the position of the object using a sinusoidal function.