A rigid block of mass M is mounted on four elastic supports, as shown in the figure below. Asmall mass m drops from a heighth and adheres to the rigid block without rebounding, andthe spring constant of each elastic support is k. Determine the equation of motion of thesystem after the small mass strikes the block. Given the following values, if the equation ofmotion is in the form + ax = 0, determine the value of a.M = 55 kg; m = 6 kg; k=181 N/m; h = 20 cm The springs are modified, so that the equation of motion is now + 14 = 0. If x = 0 at thestatic equilibrium position when both masses are included, the initial position is given by. Hence, determine the initial velocity of the system at the point of impact,* (t = 0) = V₁ (units m/s).mg204kVo =If the resulting motion of the system after the impact is of the formr(t) = A cos wnt + B sin wnt, determine the values,A =B =wn (rad/s) =KkMmkx

A rigid block of mass M is mounted on four elastic supports, as shown in the figure below. A small mass m drops from a height hand adheres to the rigid block without rebounding, and the spring constant of each elastic support is k. Determine the equation of motion of the system after the small mass strikes the block. Given the following values, if the equation of motion is in the form + az = 0, determine the value of a. M = 55 kg; m = 6 kg; k=181 N/m; h= 20 cm

A rigid block of mass M is mounted on four elastic supports, as shown in the figure below. A small mass m drops from a height hand adheres to the rigid block without rebounding, and the spring constant of each elastic support is k. Determine the equation of motion of the system after the small mass strikes the block. Given the following values, if the equation of motion is in the form + az = 0, determine the value of a. M = 55 kg; m = 6 kg; k=181 N/m; h= 20 cm

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

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

A rigid block of mass M is mounted on four elastic supports, as shown in the figure below. A
small mass m drops from a heighth and adheres to the rigid block without rebounding, and
the spring constant of each elastic support is k. Determine the equation of motion of the
system after the small mass strikes the block. Given the following values, if the equation of
motion is in the form + ax = 0, determine the value of a.
M = 55 kg; m = 6 kg; k=181 N/m; h = 20 cm

The springs are modified, so that the equation of motion is now + 14 = 0. If x = 0 at the
static equilibrium position when both masses are included, the initial position is given by
. Hence, determine the initial velocity of the system at the point of impact,
* (t = 0) = V₁ (units m/s).
mg
20
4k
Vo =
If the resulting motion of the system after the impact is of the form
r(t) = A cos wnt + B sin wnt, determine the values,
A =
B =
wn (rad/s) =
K
k
M
m
k
x

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