Mechanics for Engineers

Cover Mechanics for Engineers
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35).
At P, distant x feet from O.thework done in motion from O is \ex''; represented by the area OHP, and the kinetic energy at P is therefore represented by the area DAPH.
71. Simple Pendulum. — This name refers strictly to a particle of indefinitely small dimensions and yet having weight, suspended by a perfectly flexible weightless thread from a fixed point, about which, as a centre, it swings freely in a circular arc. In practice, a small piece of heavy metal, usually called a pendulum bob,
... suspended by a moderately long thin fibre, behaves very nearly indeed like the ideal pendulum defined above, the resistances, such as that of the atmosphere, being small.
Let 0, Fig. S3, be the point of suspension of the particle P of a simple pendulum.
Let OP, the length of thread, be /feet.
Let B = angle AOP in radians which OP makes with the vertical (OA) through O in any position P of the particle.
Draw PT perpendicular to OP, i.e. tangent to the arc of motion to meet the vertical through O in T.


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