Question 5 A fidget spinner that is 4 inches in diameter is spinning clockwise. The spinner spins at 3000
revolutions per minute.
At t = 0, consider the point A on the outer edge of the spinner that is along the positive horizontal
axis. Let h(t) be the vertical position of A in inches. Suppose t is measured in minutes. Find a
sinusoidal function that models h(t).
h(t) =

Can someone help me please ASAP?!!

Step-by-step explanation:

Solution:-

The position of any particle or object lying on a circular surface which is rotating with an angular speed of ( w ).

The motion of the particle/object can be expressed as sinusoidal or harmonic motion. We can express the motion of the particle in the cartesian coordinate system using a sinusoidal waveform.

The position of the particle/object from the central axis at time t = 0 can be given in the form:

                    h ( t ) = A*sin ( w*t )

Where,       A: The amplitude of the particle in motion ( in )

                  w: The angular frequency of rotation ( rad/s )

The amplitude ( A ) of the sinusoidal waveform is determined from the maximum displacement of the particle/object from the horizontal axis which defined by the radius of the fidget spinner where the particle is located. Hence, A = 4 in

The fidget rotates at 3000 rpm. We need to determine the angular speed of the particle. Assuming no slip conditions, the particle also rotates at 3000 rpm.

We will first convert 3000 rpm into rad/s as follows:

The sinusoidal function that models h ( t ) can be written as:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is