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# @CPhill

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The crank on a pencil sharpener's max height reaches to 3 cm above its centre axis which is 1 m off the ground and can be spun 4 times in a second. Which function models the crank height, h(t), where t is in seconds?

a) h(t)=0.03sin(8πt)+1

b) h(t)=0.03sin(4πt)+1

c) h(t)=0.3sin(8πt)+1

d) h(t) = 0.03 sin (2π/4 t)+1

Nov 29, 2017

#1
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There are 4 periods in each second

So....eaach period lasts 1/4 seconds

At t = 0,  let the height = 1 m

So...at  1/16 seconds  the max ht is reached

At 2/16 seconds the height returns to 1m

At 3/16 seconds, the min height is reached  = 1m - .03m  = .97m

And at 4/16 = 1/4 second it returns to a height of 1m

Note that the sin is maxed at pi/2

So....at  1/16 seconds....we have that  .03 sin (8pi *1 /16) + 1  =  .03sin (8pi/16) + 1  =

.03sin (pi/2) + 1 =  .03(1) + 1  =   .03 + 1  =  1.03m

So.....the function  is

h(t)   =  sin ( 8pi * t)  +  1    =   choice " a "

See the graph here :

https://www.desmos.com/calculator/f9yuhgchgr

Nov 29, 2017
edited by CPhill  Nov 29, 2017
#2
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Okay thanks :D

Julius  Nov 29, 2017
edited by Julius  Nov 29, 2017