PART A k = 2.000 N/m M=0.125kg A 0.125kg mass is attached to a horizontal spring of spring constant k = 2 N/m and set into oscillation. Assume frictionless floor. 4 rodls What is the angular frequency o of the vibration? @ = How about the vibrating frequency f in Hz? f = 0.64 Hz The position of the mass is given as x = A cos (@t + o0). With your calculated value of w, fill in the following table (don't forget to set your calculator to "radian mode"). Each row represents a different oscillation with the same spring, pay attention to sign: v (m/s) .092 - .14 a (m/s²) 3076 -32 -.8712 -.64 x (m) -.02 A (m) t (s) po (rad) F (N) .04 -.04 V 0.03 2.5 0.3 -212 1.36 0.04 0.02 0.2 0.06 .0545 0.1 0.4 ,076 1.08 -. 08 0.04 0.3 -26 - 25 -0.2 2.94 0.5 0.04 0.1 0.1 PART B Each of the rows in the following table represents an oscillation of a different spring and mass. Fill in the blanks. E is the total energy. Vmax, v, Xmax, and x are all positive in values. E (J) (rad/s) A (m) Vmax Xmax m (kg) k (N/m) x at t=0 v at t=0 (m/s) (m/s²) (m) (m/s) 0.05 20 0.01 1.0 9.0 0.3 0.5 0.15 2.0 5.0 2.0 5.0 0.6 2.0 0.6 0.2 2.0 5.0 0.1

PART A k = 2.000 N/m M=0.125kg A 0.125kg mass is attached to a horizontal spring of spring constant k = 2 N/m and set into oscillation. Assume frictionless floor. 4 rodls What is the angular frequency o of the vibration? @ = How about the vibrating frequency f in Hz? f = 0.64 Hz The position of the mass is given as x = A cos (@t + o0). With your calculated value of w, fill in the following table (don't forget to set your calculator to "radian mode"). Each row represents a different oscillation with the same spring, pay attention to sign: v (m/s) .092 - .14 a (m/s²) 3076 -32 -.8712 -.64 x (m) -.02 A (m) t (s) po (rad) F (N) .04 -.04 V 0.03 2.5 0.3 -212 1.36 0.04 0.02 0.2 0.06 .0545 0.1 0.4 ,076 1.08 -. 08 0.04 0.3 -26 - 25 -0.2 2.94 0.5 0.04 0.1 0.1 PART B Each of the rows in the following table represents an oscillation of a different spring and mass. Fill in the blanks. E is the total energy. Vmax, v, Xmax, and x are all positive in values. E (J) (rad/s) A (m) Vmax Xmax m (kg) k (N/m) x at t=0 v at t=0 (m/s) (m/s²) (m) (m/s) 0.05 20 0.01 1.0 9.0 0.3 0.5 0.15 2.0 5.0 2.0 5.0 0.6 2.0 0.6 0.2 2.0 5.0 0.1

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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Strain Gauges

All the components used in civil engineering and mechanical engineering applications undergo deformations due to induced internal stresses under the application of external loads. Under repeated application of loads, there is a high possibility of failure of the components. Hence, periodic monitoring of the components and determination of stresses are very important.

Question

PART A
k = 2.000 N/m
M=0.125kg
A 0.125kg mass is attached to a horizontal spring of spring constant k = 2 N/m and set into
ocillation. Assume frictionless floor.
4 rod /s
What is the angular frequency w of the vibration? o =
How about the vibrating frequency f in Hz? f =
0.64 Hz.
The position of the mass is given as x = A cos (ot + o). With your calculated value of w, fill in
the following table (don't forget to set your calculator to "radian mode"). Each row represents
a different oscillation with the same spring, pay attention to sign:
v (m/s)
.092
-.14
a (m/s²)
3076
-32
-.8712
-.64
A (m)
t (s)
x (m)
-.02
F (N)
.04
-.04
фо (rad)
0.03
2.5
0.3
- 212
1.36
0.04
0.02
0.2
0.06
.0545
0.1
0.4
.076
1.08
-. 08
0.04
0.3
|-26
- .25
2.94
-0.2
0.5
0.04
0.1
0.1
PART B
Each of the rows in the following table represents an oscillation of a different spring and mass.
Fill in the blanks. E is the total energy. Vmax, v, Xmax, and x are all positive in values.
A (m)
Vmax
Xmax
m (kg)
k (N/m)
E (J)
x at t=0
v at t=0
(m/s)
(m/s²)
(rad/s)
(m)
(m/s)
0.05
20
5
0.01
1.0
9.0
0.3
0.5
0.15
2.0
5.0
2.0
5.0
0.6
2.0
0.6
0.2
2.0
5.0
0.1
E

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