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webwork.uoregon.edu Napkin Holder... Netfllx Chegg Study 1 Guided S. Chegg Study Guided S. WeBWorK : Math112-33 Find A Sinusoidal Funet 2 points) A weight is suspended from the ceiling by a spring. Let d be the distance in centimeters from the ceiling to the weight. When the weight is motionless, d = 1 cm. If the weight is disturbed, it begins to bob up and down or oscillato. Then d is a periodic function of t, the time in seconds, so d-f(). Consider the graph ofd-f) below, which represents the distance of the weight from the celling at time t. (a) Based on the graph of d-f) above, which of the statements below correctly describes the motion of the weight as it bobs up and down? A. The weight starts closest to the floor and begins by bouncing up towards the ceiling B. The weight starts closest to the ceiling and begins by stretching the spring down towards the floor C. The spring starts at its average distance between the ceiling and floor and begins by stretching the spring down towards the floor D. None of the above (b) How long does it take the weight to bounce completely up and down (or down and up) and return to its starting position? Include units in your answer.) (c) What is the closest the weight gets to the ceiling? Include units in your answer) (d) What is the furthest the weights gets from the ceiling? Include units in your answer.) (o) What is the amplitdue of the graph pt d f)7 Include units in your answer)Explanation / Answer
a) based on the graph
the spring starts at its average distance between ceiling and floor
option c is correct
b) finding period of the function
it completes one cycle in 1/2 seconds
period = 1/2 seconds
so, it takes 1/2 seconds to bounce completely up and down
c) the closest weight can get to the ceiling is 7 cm
d) the farthest weight can get from the ceiling is 15 cm
e) amplitude = (15-7)/2 = 4
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