#### Kerala PSC General Science Book Study Materials Page 16

Book's First Pagedirection 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. 15

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