Answer:
[tex]h ( t ) = 4 sin ( 100\pi*t )[/tex]
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:
[tex]f= \frac{3000 rev}{min} * \frac{min}{60 s} = 50 \frac{rev}{s} \\\\w = 2\pi f\\\\w = 2\pi \frac{rad}{rev} * \frac{50 rev}{s} \\\\w = 100\pi \frac{rad}{s}[/tex]
The sinusoidal function that models h ( t ) can be written as:
[tex]h ( t ) = 4 sin ( 100\pi*t )[/tex]
