(a) A body of mass m, controlled by an elastic system, is given a displacement x.Derive an expression for the periodic frequency, n, of linear motion of the elasticsystem1n =Hz1Hzwhere ő is the static deflection in metres under the load, mg.(b) Figure TQ3.3 shows a suspended pendulum from a fixed pivot at O. The pendulumconsists of a bar B, of mass 1kg, and block C of mass 6kg. The centre of gravity G1 andG2 of B and C are at distance 150mm and 375mm from 0. The radius of gyration of Band C, each about its own centre of gravity, are respectively 100mm and 25mm. A lightspring is attached to the pendulum at point P, 200mm from 0, and is anchored at a fixedpoint, Q.When the Pendulum is in equilibrium, the line OG,PG2 is at 45° from the vertical andthe angle OPQ is 90°. The spring has a stiffness of 700N/m.Calculate the natural frequency of the pendulum for small oscillations about theequilibrium position.45°0-1500-20Ig NG2f0-3750Y6g NFigure TQ3.3

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body of mass m, elastic system, isplacement Derive an expression for the periodic frequency, n, of linear motion of the elastic system 1 Hz 1 Hz where ô is the static deflection in metres under the load, mg. (b) Figure TQ3.3 shows a suspended pendulum from a fixed pivot at O. The pendulum consists of a bar B, of mass 1kg, and block C of mass 6kg. The centre of gravity G1 and G2 of B and C are at distance 150mm and 375mm from O. The radius of gyration of B and C, each about its own centre of gravity, are respectively 100mm and 25mm. A light spring is attached to the pendulum at point P, 200mm from O, and is anchored at a fixed point Q. When the Pendulum is in equilibrium, the line OG;PG2 is at 45° from the vertical and the angle OPQ is 90°. The spring has a stiffness of 700N/m. Calculate the natural frequency of the pendulum for small oscillations about the equilibrium position. 0-150 K020 G2 tog N

body of mass m, elastic system, isplacement Derive an expression for the periodic frequency, n, of linear motion of the elastic system 1 Hz 1 Hz where ô is the static deflection in metres under the load, mg. (b) Figure TQ3.3 shows a suspended pendulum from a fixed pivot at O. The pendulum consists of a bar B, of mass 1kg, and block C of mass 6kg. The centre of gravity G1 and G2 of B and C are at distance 150mm and 375mm from O. The radius of gyration of B and C, each about its own centre of gravity, are respectively 100mm and 25mm. A light spring is attached to the pendulum at point P, 200mm from O, and is anchored at a fixed point Q. When the Pendulum is in equilibrium, the line OG;PG2 is at 45° from the vertical and the angle OPQ is 90°. The spring has a stiffness of 700N/m. Calculate the natural frequency of the pendulum for small oscillations about the equilibrium position. 0-150 K020 G2 tog N

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Question

(a) A body of mass m, controlled by an elastic system, is given a displacement x.
Derive an expression for the periodic frequency, n, of linear motion of the elastic
system
1
n =
Hz
1
Hz
where ő is the static deflection in metres under the load, mg.
(b) Figure TQ3.3 shows a suspended pendulum from a fixed pivot at O. The pendulum
consists of a bar B, of mass 1kg, and block C of mass 6kg. The centre of gravity G1 and
G2 of B and C are at distance 150mm and 375mm from 0. The radius of gyration of B
and C, each about its own centre of gravity, are respectively 100mm and 25mm. A light
spring is attached to the pendulum at point P, 200mm from 0, and is anchored at a fixed
point, Q.
When the Pendulum is in equilibrium, the line OG,PG2 is at 45° from the vertical and
the angle OPQ is 90°. The spring has a stiffness of 700N/m.
Calculate the natural frequency of the pendulum for small oscillations about the
equilibrium position.
45°
0-150
0-20
Ig N
G2
f0-3750
Y6g N
Figure TQ3.3

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