Question

Statement 1: If the amplitude of a simple harmonic oscillator is doubled, its total energy becomes four times.
Statement 2: The total energy is directly proportional to the square of the amplitude of vibration of the harmonic oscillator.

• A. Statement 1 is false, Statement 2 is true
• B. Statement 1 is true, Statement 2 is true; Statement 2 is the correct explanation for Statement 1
• C. Statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement 1
• D. Statement 1 is true, Statement 2 is false

Answer 1

Answer: (B)

Statement 1 is true, Statement 2 is true; Statement 2 is the correct explanation for Statement 1

$T=\frac{1}{2}m{A}^2{\omega }^2$
Thus, $T\propto A^2$
Hence both statements are correct and statement 2 is correct explanation of statement 1.