An object of mass 10g executes SHM along the x -axis with frequency of ( 10 ) Hz. At the point x = 2 cm the object has KE 1.2 J and PE 0.4 J. The amplitude of oscillation is

Step-by-step solution

Given, Kinetic Energy ( KE ) = 1.2 J and Potential Energy ( PE ) = 0.4 J at displacement x = 2 cm. The total energy ( E ) of the object executing SHM is the sum of its kinetic and potential energies: E = KE + PE = 1.2 + 0.4 = 1.6 J In simple harmonic motion, the potential energy at a displacement x and the total energy are given by: PE = 1 2 m ^2 x^2 E = 1 2 m ^2 A^2 Taking the ratio of total energy to potential energy: E PE = A^2 x^2 Substituting the given values: 1.6 0.4 = A^2 2^2 4 = A^2 4 A^2 = 16 A = 4 cm Answ