```   direction opposite to the gravitational             Simple Pendulum
acceleration,
  p is the pressure at the chosen point, and              The period of swing of a simple gravity
    is the density of the fluid at all points in          pendulum depends on its length, the local
the fluid.                                               strength of gravity, and to a small extent
on the maximum angle that the pendulum
Periodic Motion                                             swings away from vertical, θ0, called the
amplitude.
  It is the motion repeated in equal intervals            It is independent of the mass of the body.
of time.                                                 If the amplitude is limited to small swings,
  It is performed, for example, by a rocking               the period T of a simple pendulum, the
chair, a bouncing ball, and a vibrating                  time taken for a complete cycle, is:
tuning fork, a swing in motion, the Earth
in its orbit around the Sun, and a water                          L
T  2       0 1 (1)
wave.                                                             g
Simple harmonic motion                                 Where,
  It is the back and forth motion that is             T is the period in seconds (s)
caused by a force that is directly
proportional to the displacement. The               L is the length of the rod or wire in meters or
displacement centers on an equilibrium              feet
position.
   FS  x                                             g is the acceleration due to gravity (9.8 m/s2)
   FS  kx or  kx
For small swings the period of swing is
  k = Constant of Proportionality
approximately the same for different size
  k = Spring Constant(Unit : N/m)                     swings: that is, the period is independent of
  One of the simplest type of simple                  amplitude. This property, called isochronism,
harmonic motion is called Hooke"s Law.              is the reason pendulums are so useful for
This is primarily in reference to springs.          timekeeping. Successive swings of the
  The negative sign only tells us that “F” is         pendulum, even if changing in amplitude, take
what is called a restoring force, in that it        the same amount of time.
works in the opposite direction of the
displacement.                                       For larger amplitudes, the period increases
gradually with amplitude so it is longer than
Oscillatory Motion                                     given by equation (1). For example, at an
amplitude of θ0 = 23° it is 1% larger than
  It is a motion that repeats itself in a regular     given by (1). The period increases
cycle for example a sine wave or                    asymptotically (to infinity) as θ0 approaches
pendulum.                                           180°, because the value θ0 = 180° is an
  The time taken for an oscillation to occur          unstable equilibrium point for the pendulum.
is often referred to as the oscillatory
period.
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