A weight is attached to a spring suspended from a beam. At time t = 0, it is pulled down to a point 8 cm above the ground and released. After that, it bounces up and down between its minimum height of 8 cm and a maximum height of 24 cm, and its height h(t) is a sinusoidal function of time t. It first reaches a maximum height 1.4 seconds after starting. (a) Follow the procedure outlined in this section to sketch a rough graph of h(t). Draw at least two complete cycles of the oscillation, indicating where the maxima and minima occur. (b) What are the mean, amplitude, phase shift and period for this function? (Use a phase shift with an absolute value less than the period.) mean 16 amplitude 8 phase shift _ period 2.8 (c) Give four different possible values for the phase shift. (Enter your answers as a comma-separated list.) _ (d) Write down a formula for the function h(t) in standard sinusoidal form; i.e. as in the equation shown below. h(t) = A sin 2? B(t − C) + D h(t) = 8sin((2.8x−1)+16) (e) What is the height of the weight after 4.2 seconds? _cm (f) During the first 10 seconds, how many times will the weight be exactly 19 cm above the floor? (Note: This problem does not require inverse trigonometry.)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A weight is attached to a spring suspended from a beam. At time t = 0, it is pulled down to a point 8 cm above the ground and released. After that, it bounces up and down between its minimum height of 8 cm and a maximum height of 24 cm, and its height

h(t)

is a sinusoidal function of time t. It first reaches a maximum height 1.4 seconds after starting.

(a) Follow the procedure outlined in this section to sketch a rough graph of

h(t).

Draw at least two complete cycles of the oscillation, indicating where the maxima and minima occur.

(b) What are the mean, amplitude, phase shift and period for this function? (Use a phase shift with an absolute value less than the period.)

mean	16
amplitude	8
phase shift	___
period	2.8

_______

(d) Write down a formula for the function

h(t)

in standard sinusoidal form; i.e. as in the equation shown below.

h(t) = A sin

(t − C)

+ D

h(t) = ____

8sin((2.8x−1)+16)

(e) What is the height of the weight after 4.2 seconds?
_____cm

(f) During the first 10 seconds, how many times will the weight be exactly 19 cm above the floor? (Note: This problem does not require inverse trigonometry.)

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