Answer:
A
simple pendulum is simply a heavy mass (often called bob) suspended by an inextensible
string whose other end is tied to a rigid support S.
When bob of the pendulum is at extreme position A, its height is H above
the mean position O; so it has potential energy equal to mgH(with no kinetic energy)
so its total energy is also mgH. As the bob of pendulum swings from A to O, its
height decreases and so its potential energy is converted into kinetic energy.
At point O, its potential energy is zero and kinetic energy is maximum.
At equilibrium position O, its total energy is in the form
of kinetic energy. If is the speed of bob at O,
then its kinetic energy at . At O bob has
velocity towards end B, so due to inertia it swings towards B; in this duration
its height again increases and its kinetic energy is converted into potential
energy. At extreme position B, its kinetic energy becomes zero and its
potential energy is maximum again equal to mgH which is also equal to total
energy. At B, the particle is momentarily at rest and due to restoring force
directed towards O, it again swings from B to A; its potential energy decreases
and kinetic energy increases. At O, potential energy is again zero and kinetic
energy is maximum; thus, again at O, its total energy is in the form of kinetic
energy. Now at O its velocity is towards end A and due to inertia it moves
towards A. During this period, its kinetic energy is again converted into
potential energy, which becomes maximum equal to height at A. Thus, at A it has
total energy in the form of potential energy. This completes one oscillation of
pendulum. At A, it is momentarily at rest and due to restoring force now
directed towards O, it again swings towards O and the process is repeated.
Thus, in simple pendulum, the potential energy is converted into kinetic energy
and vice versa, so that total energy is constant at every position of bob.
Total energy of swinging bob
= Potential energy at extreme position (A or B) = mgH
= Kinetic energy at mean position
At any intermediate position such as P or Q, it has partly
kinetic energy and partly potential energy, but sum of both energies remains
constant equal to
When the bob of a simple pendulum oscillates in air, the
air friction opposes its motion. As the bob of pendulum strikes the air
molecules, the kinetic energy of the bob is converted into heat energy. The amplitude
of pendulum decreases and finally it stops. Here, one form of energy is
converted into another form of energy, so the law of conservation of energy is
not violated.
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