A body of mass 100 g is executing simple harmonic motion with an amplitude of 0.1 m and a time period of seconds. The total mechanical energy of the oscillating system is :

Step-by-step solution

The total mechanical energy E of a body executing simple harmonic motion is given by: E = 1 2 m ^2 A^2 where m is the mass, is the angular frequency, and A is the amplitude. Given: Mass, m = 100 g = 0.1 kg Amplitude, A = 0.1 m Time period, T = s First, calculate the angular frequency : = 2 T = 2 = 2 rad/s Now, substitute the values into the energy formula: E = 1 2 0.1 (2)^2 (0.1)^2 E = 1 2 0.1 4 0.01 E = 0.2 0.01 = 0.002 J. Answer: 0.002 J