Introductory Mathematics for Engineering Applications
Introductory Mathematics for Engineering Applications
1st Edition
ISBN: 9781118141809
Author: Nathan Klingbeil
Publisher: WILEY
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Chapter 6, Problem 30P

A pair of springs and masses vibrate under simple harmonic motion, as shown in Fig. P6.30. The positions of the masses in inches are given by y 1 ( t ) = 5 2 cos ( 2 π t + π 4 ) and y 2 ( t ) = 10 cos ( 2 π t ) , where t is in seconds.

(a) Write down the amplitude, frequency (in Hz), period (in seconds) phase shift (in degrees), and time shift (in seconds) of the position of the first mass y 1 ( t ) .

(b) Plot one cycle of the position y 1 ( t ) , and indicate the earliest time alter t = 0 when the position is zero.

(c) The vertical distance between the two masses is given by δ ( t ) = y 1 ( t ) y 2 ( t ) , Write δ ( t ) in the form δ ( t ) = M sin ( 2 π t + θ ° ) ; in other words, find M and θ .

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Chapter 6 Solutions

Introductory Mathematics for Engineering Applications

Ch. 6 - A spring-mass system is displaced x=10 cm and let...Ch. 6 - Suppose the spring-mass system of problem P6-11 is...Ch. 6 - Figure P.13 A spring-mass system for problem...Ch. 6 - The position of a spring-mass system shown in Fig....Ch. 6 - The position of a spring-mass system shown in Fig....Ch. 6 - A simple pendulum of length L=100 cm is shown in...Ch. 6 - Repeat problem P6-16 if L=10 in, and...Ch. 6 - A sinusoidal current i(t)=0.1sin(100t) amps is...Ch. 6 - A sinusoidal current i(t)=200cos(120t+14.86) mA is...Ch. 6 - A series RL circuit is subjected to a sinusoidal...Ch. 6 - A series RL circuit is subjected to a sinusoidal...Ch. 6 - A sinusoidal voltage (t)=10sin(1000t)V is applied...Ch. 6 - A parallel RL circuit is subjected to a sinusoidal...Ch. 6 - A parallel RL circuit is subjected to a sinusoidal...Ch. 6 - Consider the RC circuit shown in Fig. P6.25, where...Ch. 6 - Consider the RC circuit shown in Fig.P6.25, where...Ch. 6 - Two voltages 1(t)=10sin(100t45)V and...Ch. 6 - Repeat problem P6-27 if 1(t)=10cos(100t+90)V and...Ch. 6 - Two voltages 1(t)=102sin(500t34)V and...Ch. 6 - A pair of springs and masses vibrate under simple...Ch. 6 - Suppose the positions of the masses in problem...Ch. 6 - Two oscillating masses are connected by a spring...Ch. 6 - Now assume that the positions of two masses in...Ch. 6 - A manufacturing plant employs a heater and a...Ch. 6 - Repeat problem P6-34 if H(t)=100sin(120t)V and...Ch. 6 - In the three-phase circuit shown in Fig.P.36....Ch. 6 - In the three-phase circuit shown in Fig.P.36....Ch. 6 - In the three-phase circuit shown in Fig.P.36....Ch. 6 - The Hip implant shown in Fig. P6.39 is subjected...Ch. 6 - Repeat problem P6-3 if F(t)=15sin(10t)+75N.
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