Problem. A block with a mass of 15 kg sits on the smooth incline shown below where the angle is e = 37°. The block is attached to the wall via a spring with a spring constant of k = 246 N/m. The coordinate system for this problem is oriented as shown in the diagram. Based on this information, answer the following: a) Determine the distance the spring must stretch to offset the weight component of the block in the x-direction (this is where your x-direction datum will be located). b) Create a free body diagram and use the force balance in the x-direction to develop the second-order ordinary differential equation governing the motion of the block (your force balance should be based upon the datum found in part a). c) Find the natural frequency (Wn), the period of vibration (T), and the frequency (f). d) For an undamped, freely vibrating system the solution to the second-order ordinary differential equation developed in part b has the form x(t) = Asin(wnt) + Bcos(wnt). If at

Problem. A block with a mass of 15 kg sits on the smooth incline shown below where the angle is e = 37°. The block is attached to the wall via a spring with a spring constant of k = 246 N/m. The coordinate system for this problem is oriented as shown in the diagram. Based on this information, answer the following: a) Determine the distance the spring must stretch to offset the weight component of the block in the x-direction (this is where your x-direction datum will be located). b) Create a free body diagram and use the force balance in the x-direction to develop the second-order ordinary differential equation governing the motion of the block (your force balance should be based upon the datum found in part a). c) Find the natural frequency (Wn), the period of vibration (T), and the frequency (f). d) For an undamped, freely vibrating system the solution to the second-order ordinary differential equation developed in part b has the form x(t) = Asin(wnt) + Bcos(wnt). If at

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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Concept explainers

Forming and Shaping

Metal forming is a category of metalworking process through which the material can be given the desired shape and size by subjecting it to plastic deformation, where the component undergoes bulk deformation process upon application of loads. Unlike the shearing and machining process, the material does not undergo up to a failure point as indicated in the stress-strain curve. Hence, the stresses induced during the forming process are greater than yield strength but less than the failure strength of the material. The process does not lead to the loss of material, so it can be said to be an economical process. During forming, the material is subjected to tensile forces, compressive forces, bending, and shearing loading conditions. The material should possess the property of ductility to undergo the forming process.

Question

Problem
A block with a mass of 15 kg sits on the smooth incline shown below
where the angle is e = 37°. The block is attached to the wall via a spring with a spring constant
of k = 246 N/m. The coordinate system for this problem is oriented as shown in the diagram.
Based on this information, answer the following:
a) Determine the distance the spring must stretch to offset the weight component of the
block in the x-direction (this is where your x-direction datum will be located).
b) Create a free body diagram and use the force balance in the x-direction to develop the
second-order ordinary differential equation governing the motion of the block (your
force balance should be based upon the datum found in part a).
c) Find the natural frequency (wn), the period of vibration (T), and the frequency (f).
d) For an undamped, freely vibrating system the solution to the second-order ordinary
differential equation developed in part b has the form x(t) = Asin(wnt) + Bcos(wnt). If at
time t = 0 s the block is displaced to x = -0.7 m and has a velocity of v = 1.3 m/s, find the
value of the unknown coefficients A and B.
e) Calculate the position of the block att= 5.25 s.
Frictionless
surface

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