For a simple pendulum, having time period T , the variation of kinetic energy (K.E.) with time (t) is represented by :

Step-by-step solution

The displacement of a simple pendulum executing simple harmonic motion is given by x = A ( t + ) . The velocity of the pendulum is v = dx dt = A ( t + ) . The kinetic energy is given by K = 1 2 m v^2 = 1 2 m A^2 ^2 ^2( t + ) . Since kinetic energy is proportional to the square of velocity, it can never be negative. This eliminates the graphs that show negative values. Also, the kinetic energy of a pendulum is not constant, which eliminates the constant graph. Using the trigonometric identity ^2 = 1 + (2 ) 2 , we ge