(b) A fragile instrument which comprises of two masses m1 = 50 kg and m2 = 200 kg is connected by a rigid massless horizontal rod of length, I=1 m as shown in Figure Q3. The masses are suspended by four identical springs, each with stiffness, k = 1000 N/m. Assume that the instrument behaves in coupling coordinate free vibration system; (i) Sketch the free body diagram of the system by including the location of center of gravity and values of l1 and l2. (ii) Derive the equations of motion of the system in matrix form [M]{x}+ [K]{x} = 0 by including all the values of m1, m2, l1 and l2. (iii) Find the natural frequencies and mode shapes of the system.
(b) A fragile instrument which comprises of two masses m1 = 50 kg and m2 = 200 kg is connected by a rigid massless horizontal rod of length, I=1 m as shown in Figure Q3. The masses are suspended by four identical springs, each with stiffness, k = 1000 N/m. Assume that the instrument behaves in coupling coordinate free vibration system; (i) Sketch the free body diagram of the system by including the location of center of gravity and values of l1 and l2. (ii) Derive the equations of motion of the system in matrix form [M]{x}+ [K]{x} = 0 by including all the values of m1, m2, l1 and l2. (iii) Find the natural frequencies and mode shapes of the system.
Elements Of Electromagnetics
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Question
![(b) A fragile instrument which comprises of two masses m1 = 50 kg and m2 = 200 kg is
connected by a rigid massless horizontal rod of length, I=1 m as shown in Figure
Q3. The masses are suspended by four identical springs, each with stiffness, k =
1000 N/m. Assume that the instrument behaves in coupling coordinate free vibration
system;
(i)
Sketch the free body diagram of the system by including the location of
center of gravity and values of l, and l2.
(ii)
Derive the equations of motion of the system in matrix form
[M]{x}+ [K]{x} = 0 by including all the values of m1, m2, l1 and l2.
(iii) Find the natural frequencies and mode shapes of the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f1e8e29-c224-4dc0-b533-9e5d4dacb769%2Faf10e99c-b6af-4dca-8b27-e70cd20c4047%2F2ktj51_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) A fragile instrument which comprises of two masses m1 = 50 kg and m2 = 200 kg is
connected by a rigid massless horizontal rod of length, I=1 m as shown in Figure
Q3. The masses are suspended by four identical springs, each with stiffness, k =
1000 N/m. Assume that the instrument behaves in coupling coordinate free vibration
system;
(i)
Sketch the free body diagram of the system by including the location of
center of gravity and values of l, and l2.
(ii)
Derive the equations of motion of the system in matrix form
[M]{x}+ [K]{x} = 0 by including all the values of m1, m2, l1 and l2.
(iii) Find the natural frequencies and mode shapes of the system.

Transcribed Image Text:k
k
12
Rigid box
50 kg
200 kg
to
x(t)
y(t) = 0.02 sin 3t
k
k
Truck bed
Figure Q3
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