A particle executing simple harmonic motion has a time period of 4 s and an amplitude of 6 m . If it starts its motion from the positive extreme position at t = 0 , the equation of its displacement x as a function of time t is

Step-by-step solution

Given, time period T = 4 s and amplitude A = 6 m . The angular frequency is given by: = 2 T = 2 4 = 2 rad/s The general equation for the displacement of a particle in SHM is: x = A ( t + ) Since the particle starts from the positive extreme position at t = 0 , its initial phase = 2 . Substituting the values into the general equation: x = 6 ( t 2 + 2 ) Using the trigonometric identity ( + 2 ) = ( ) , we get: x = 6 ( t 2 ) Answer: x = 6 ( t 2 )