Answered: A 1-kg mass is attached to a spring…

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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Question

B and c

A 1-kg mass is attached to a spring with stiffness 1 N/m. The damping constant for the suystem is 2 N-sec/m. At time t=0, the mass is compressed 20 cm (=0.2 m) to the left and given an initial
velocity of 30 cm/sec (=0.3 m/sec) to the right.
(a) The position x(t) of the mass at time t is given by
OA.
sint -2 cos t
10
OB.
O C.
x(t) =
2-t
x(t)= et
10
x(t) =
1-2
10
-t
-t

(b) When for the first time the mass passes through the equilibrium position?
OA.
t=
OB. The mass never passes through the equilibrium position
O C.
OB.
t=
OD. t = 2
OE. None of the given answers is correct
O D.
(c) What is the maximum displacement to the right that the mass will attain?
O A.
K
6
e
I
3
10
-3
1
10
(meters)
元
2
e (meters)
OC. 2 -4
e
10
e
(meters)
Л
√3
(meters)
30
OE. None of the given answers is correct
6

Expert Solution

Step 1

Given data:

$\begin{array}{rcl} mass (m) & = & 1 kg \\ spring stiffness (k) & = & 1 N / m \\ damping constant (c) & = & 2 N \sec / m \\ initial velocity (v) & = & 30 cm / \sec \\ compressed length (l) & = & 20 cm \end{array}$

Find out:

(a). Position of mass at time (t).

(b). When for the first time the mass passes through the equilibrium position.

(c). When the maximum displacement to the right that the mass will attain.

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