Homework Answers
In this solution some basic concepts of Vibration Mechanics are used. For more information, refer to any standard textbook or drop a comment below. Please give a positive rating if solution is helpful.
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Problem 1: Axial vibrations of a rod The rod of length L is fixed at ends x = 0 and x = L. The de...
(10 pts) The mode shape of a uniform rod of length L fixed at both ends in axial vibration is 1. ...
(10 pts) The mode shape of a uniform rod of length L fixed at both ends in axial vibration is 1. e,(x)-a,sin/m) Find the value of the coefficient a, such that the mode is orthonormal. Assume the mass per unit length of the rod is m
(10 pts) The mode shape of a uniform rod of length L fixed at both ends in axial vibration is 1. e,(x)-a,sin/m) Find the value of the coefficient a, such that the mode is...
Problem 2: Hanging cable A cable of uniform mass per unit length p(x)-ρ constant, hangs freely fr...
Problem 2: Hanging cable A cable of uniform mass per unit length p(x)-ρ constant, hangs freely from the ceiling as shown in the figure. Assume that the cable possesses no flexural stiffness. Derive the equation of motion for small horizontal vibrations y(x, t) of the cable as well as the associated boundary conditions.
Problem 2: Hanging cable A cable of uniform mass per unit length p(x)-ρ constant, hangs freely from the ceiling as shown in the figure. Assume that the...
. The system shown below consists of a homogeneous rigid rod with mass m, length l,...
. The system shown below consists of a homogeneous rigid rod with mass m, length l, and mass center of gravity G where the mass moment of inertia of the rod about G is given by: Translational spring with stiffness k supports the rod at point B, and rotational damper c, İs connected to the rod at its pivot point A as shown.ft) is an external force applied to the rod. Derive the equation of motion of the single degree...
A rod of mass M and length L pivots at x=0, the rod is not uniform...
A rod of mass M and length L pivots at x=0, the rod is not uniform in density and follows the equation e=1+x (kg/m). What is the momentum of inertia in the rod
A massless rod with length L is attached to two springs at its two masses (both...
A massless rod with length L is
attached to two springs at its two masses (both m) at its two ends.
The masses are connected to springs. The springs can move in the
horizontal and vertical directions as shown in the figure and they
both have a stiffness k. Note that gravity acts. Assume the springs
are un-stretched when the rod is vertical. Find the equation of
motion for the system using 1. Newton’s second law 2. Conservation
of energy....
44. The system shown in Fig. P7 consists of a slider block of mass m2 and a uniform slender rod of mass m3, length 13, and mass moment of inertia about its center of mass J The slider block is connec...
44. The system shown in Fig. P7 consists of a slider block of mass m2 and a uniform slender rod of mass m3, length 13, and mass moment of inertia about its center of mass J The slider block is connected to the ground by a spring that has a stiffness coefficient k. The slider block is subjected to the force F(t), while the rod is subjected to the moment M. Obtain the differential equations of motion of this two-degree-of-freedom...
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid rod of length is supported as a pendulum at end A, and has a mass m. The rod...
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid rod of length is supported as a pendulum at end A, and has a mass m. The rod is also pinned to a roller and held in place by two elastic springs with constants k .
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid...
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at the other end. A mass m is attached 1/3 of the length from the hinge and a dashpot having a hinge. Ignore the ma...
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at the other end. A mass m is attached 1/3 of the length from the hinge and a dashpot having a hinge. Ignore the mass of the rod, spring and damper (a) Derive the equation of motion for the system (101
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at...
Figure 1 shows a system comprising a bar with mass m=12 kg and the length of...
Figure 1 shows a system comprising a bar with mass m=12 kg and
the length of the bar L=2 m, two springs with stiffness k_t=1000
N-m/rad and k=2000 N/m, one damper with damping coefficient c=50
N-s/m and two additive masses at the end of the bar, where each
mass (M) is equal to 50 kg. The rotation about the hinge A,
measured with respect to the static equilibrium position of the
system is θ(t). The system is excited by force...
(10 pts) The mode shape of a uniform rod of length L fixed at both ends in axial vibration is 1. e,(x)-a,sin/m) Find the value of the coefficient a, such that the mode is orthonormal. Assume the mass per unit length of the rod is m
(10 pts) The mode shape of a uniform rod of length L fixed at both ends in axial vibration is 1. e,(x)-a,sin/m) Find the value of the coefficient a, such that the mode is...
Problem 2: Hanging cable A cable of uniform mass per unit length p(x)-ρ constant, hangs freely from the ceiling as shown in the figure. Assume that the cable possesses no flexural stiffness. Derive the equation of motion for small horizontal vibrations y(x, t) of the cable as well as the associated boundary conditions.
Problem 2: Hanging cable A cable of uniform mass per unit length p(x)-ρ constant, hangs freely from the ceiling as shown in the figure. Assume that the...
. The system shown below consists of a homogeneous rigid rod with mass m, length l, and mass center of gravity G where the mass moment of inertia of the rod about G is given by: Translational spring with stiffness k supports the rod at point B, and rotational damper c, İs connected to the rod at its pivot point A as shown.ft) is an external force applied to the rod. Derive the equation of motion of the single degree...
A massless rod with length L is
attached to two springs at its two masses (both m) at its two ends.
The masses are connected to springs. The springs can move in the
horizontal and vertical directions as shown in the figure and they
both have a stiffness k. Note that gravity acts. Assume the springs
are un-stretched when the rod is vertical. Find the equation of
motion for the system using 1. Newton’s second law 2. Conservation
of energy....
44. The system shown in Fig. P7 consists of a slider block of mass m2 and a uniform slender rod of mass m3, length 13, and mass moment of inertia about its center of mass J The slider block is connected to the ground by a spring that has a stiffness coefficient k. The slider block is subjected to the force F(t), while the rod is subjected to the moment M. Obtain the differential equations of motion of this two-degree-of-freedom...
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid rod of length is supported as a pendulum at end A, and has a mass m. The rod is also pinned to a roller and held in place by two elastic springs with constants k .
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid...
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at the other end. A mass m is attached 1/3 of the length from the hinge and a dashpot having a hinge. Ignore the mass of the rod, spring and damper (a) Derive the equation of motion for the system (101
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at...
Figure 1 shows a system comprising a bar with mass m=12 kg and
the length of the bar L=2 m, two springs with stiffness k_t=1000
N-m/rad and k=2000 N/m, one damper with damping coefficient c=50
N-s/m and two additive masses at the end of the bar, where each
mass (M) is equal to 50 kg. The rotation about the hinge A,
measured with respect to the static equilibrium position of the
system is θ(t). The system is excited by force...
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Amplitude=3;
fs=8000;
n=0:399;
t=0:1/fs: n*1/fs-1/fs;
signal=3+3*cos(2*pi*1100*t)+3*cos(2*pi*2200*t)+3*cos(2*pi*3300*t);
fftSignal= fft(signal);
fftSignal=f ftshift (fftSignal);
f=fs/2*linspace(-1,1,fs);
plot(f,abs(fftsignal);
xlabel('Frequency(Hz)’)
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