Periodic Functions (sinusoidal (gr.11))

[vikasd]

Hi, i actually have 2 questions. please solve either or both for me ASAP. im working on other questions so i hope someone can solve these for me ,thanks so much.

1. A person is riding on a ferris wheel that turns at a constant speed. The lowest point of the wheel is 1 m above ground level. Another person is standing at the side of the wheel on a platform 4 m above the ground. She notes the times the person on the wheel is at the same level as she is. The intervals between two successive times are alternately 6s and 18s.
a) what is ther period of the rotation of the ferris wheel?
b) what is the radius of the wheel?


2. A bike has wheels with radius 30 cm. The bike moves along the road at a speed of 6 m/s.
a) determine the period of the rotation of the tire, that is, the time required for the tire to make one complete revolution.
b) the outside of the tire has some paint on it. Determine the equation for the height, h(t),meters of the paint point above the road as a function of time, t seconds. Assume the paint point is at its highest point when t=0.
c) sketch the graph of h(t) versus t.

 

[skeeter]

Hi, i actually have 2 questions. please solve either or both for me ASAP. im working on other questions so i hope someone can solve these for me ,thanks so much.

when you get finished with the "other" questions, show what you've done to solve these two problems and I'm sure someone will lend a hand.

 

[vikasd]

on question # 2.a) with the bike period of rotation i got: angular speed = v/r = 6/.3 = 20 revolutions/second. T= 1/20 = 0.05 sec. then period = 0.05 seconds. but i have trouble now on part b) where i need to make an equation for the paint spot, i got the equation to be
h(t) = sin7200t, not sure if im right for this or even part a).

 

[Deleted member 4993]

on question # 2.a) with the bike period of rotation i got: angular speed = v/r = 6/.3 = 20 revolutions/second. T= 1/20 = 0.05 sec. then period = 0.05 seconds. but i have trouble now on part b) where i need to make an equation for the paint spot, i got the equation to be
h(t) = sin7200t,

The equation of motion would be "sine" (or "cosine") curve shifted up by radius (because the paint-spot cannot have a negative height from the ground).

It's amplitude would be the radius and the time period would be same as that of the wheel.


not sure if im right for this or even part a).

 

[vikasd]

is the period = 0.05 seconds for the #2.a) . for #2.b) im not sure about the formula. amplitude = max - min / 2. radius is 0.3m so max would be 0.3 - min -0.3 / 2 = 0.3, so A = 0.3? then K = 360/Period = 360/0.05 = 7200. im confused

 

[skeeter]

is the period = 0.05 seconds for the #2.a) . for #2.b) im not sure about the formula. amplitude = max - min / 2. radius is 0.3m so max would be 0.3 - min -0.3 / 2 = 0.3, so A = 0.3? then K = 360/Period = 360/0.05 = 7200. im confused

2(a) ... first of all, angular velocity,
\(\displaystyle \omega = \frac{v}{r}\)
is in units of radians per second, not revolutions per second. So, period (T) is
\(\displaystyle T = \frac{2\pi}{\omega} = \frac{2\pi r}{v}\)

2(b) ... for h in meters, t in seconds
\(\displaystyle h = 0.3[1 + \cos(\omega t)]\)