For the spring-mass-damper system shown to the right, x is measured from the static equi- librium position, and the surface is friction- less. a) Determine the governing equations of m motion. 6 k 2 c b) What is the period of each oscilla- tion in terms of the system parameters (т, k, с)? c) For what value of c is the system criti- cally damped? d) If the system is released with the initial conditions: x(0) = 0.0 m, à (0) = 5.0 m/s, find the resulting solution x(t) if m = 2 kg, k = 48 N/m and c= 4 N/(m/s).

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Problem 1.
For the spring-mass-damper system shown to
the right, x is measured from the static equi-
librium position, and the surface is friction-
手
less.
a) Determine the governing equations of
m
motion.
6 k
2 c
b) What is the period of each oscilla-
tion in terms of the system parameters
(т, k, с)?
For what value of c is the system criti-
cally damped?
d) If the system is released with the initial
conditions:
x(0) = 0.0 m,
à (0) = 5.0 m/s,
find the resulting solution x(t) if m =
2 kg, k = 48 N/m and c= 4 N/(m/s).
Transcribed Image Text:Problem 1. For the spring-mass-damper system shown to the right, x is measured from the static equi- librium position, and the surface is friction- 手 less. a) Determine the governing equations of m motion. 6 k 2 c b) What is the period of each oscilla- tion in terms of the system parameters (т, k, с)? For what value of c is the system criti- cally damped? d) If the system is released with the initial conditions: x(0) = 0.0 m, à (0) = 5.0 m/s, find the resulting solution x(t) if m = 2 kg, k = 48 N/m and c= 4 N/(m/s).
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