Problem 2. A uniform bar of mass m is pivoted at point O and supported at the ends by two springs, as shown in Figure 2. End P of spring PQ is subjected to a sinusoidal displacement, x(t) = x,sinwt. 1=1 m, k=1000 N/m, m=10 kg, xo=1 cm, and w=10 rad/s. a) Drive the equations of motion and find the natural frequency of the bar b) Find the steady-state angular displacement of the bar Simulate the system and plot displacements for the following cases (choose suitable simulation time for each case): 1) With the initial conditions theta0=thetad0=0, an excitation x=xsin(w) Is applied vertically at point P. Choose such w values so that the system is i. in resonance. ii. experiencing beating. nt (1) = xp sin wt Uniform bar, mass m Figure 2. Spring-mass system

Problem 2. A uniform bar of mass m is pivoted at point O and supported at the ends by two springs, as shown in Figure 2. End P of spring PQ is subjected to a sinusoidal displacement, x(t) = x,sinwt. 1=1 m, k=1000 N/m, m=10 kg, xo=1 cm, and w=10 rad/s. a) Drive the equations of motion and find the natural frequency of the bar b) Find the steady-state angular displacement of the bar Simulate the system and plot displacements for the following cases (choose suitable simulation time for each case): 1) With the initial conditions theta0=thetad0=0, an excitation x=xsin(w) Is applied vertically at point P. Choose such w values so that the system is i. in resonance. ii. experiencing beating. nt (1) = xp sin wt Uniform bar, mass m Figure 2. Spring-mass system

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

Problem 2.
A uniform bar of mass m is pivoted at point O and supported at the ends by two springs, as shown in
Figure 2. End P of spring PQ is subjected to a sinusoidal displacement, x(t) = x,sinwt.
1=1 m, k=1000 N/m, m=10 kg, xo=1 cm, and w=10 rad/s.
a) Drive the equations of motion and find the natural frequency of the bar
b) Find the steady-state angular displacement of the bar
Simulate the system and plot displacements for the following cases (choose suitable simulation
Vont
time for each case):
1) With the initial conditions theta0=thetad0=0, an excitation xEsin(wi) Is applied vertically
at point P. Choose such w values so that the system is
i. in resonance,
exPeriencing beating.
do
D
ii.
(1) = xo sin wt
Uniform bar,
mass m
31
Figure 2. Spring-mass system

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