In simple harmonic motion, the total mechanical energy of a spring-mass system is E = 1 2 m ^2 A^2 . Suppose the oscillating particle is swapped out for another particle having double the mass, while the amplitude A is kept unchanged. The new mechanical energy will

Step-by-step solution

The total mechanical energy of a spring-mass system is given by E = 1 2 m ^2 A^2 . For a spring-mass system, the angular frequency is = k m , which gives m ^2 = k , where k is the spring constant. Substituting this into the energy expression gives E = 1 2 k A^2 . The spring constant k is a property of the spring and is independent of the mass of the oscillating particle. Since the amplitude A is kept unchanged, the total mechanical energy depends only on k and A . Therefore, the new mechanical energy will remain E