In simple harmonic motion, the total mechanical energy of the given system is \( E \). If the mass of the oscillating particle \( P \) is doubled, then the new energy of the system for the same amplitude is:
For a simple harmonic oscillator, the total mechanical energy (T.E.) is defined as: \[ T.E. = \frac{1}{2}kA^2, \] where \( k \) represents the spring constant and \( A \) denotes the amplitude of oscillation.
- Given that the amplitude \( A \) is constant, the total mechanical energy (T.E.) will also remain constant, as it is solely dependent on \( k \) and \( A \), and not on the mass \( m \) of the oscillating particle.
Consequently, doubling the mass of \( P \) will not alter the total mechanical energy \( E \).
