Question

Statement 1: The graph between velocity and displacement for a harmonic oscillator is an ellipse.
Statement 2: Velocity does not change uniformly with displacement in harmonic motion.

• 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

The correct option is C Statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement 1

$x=Asin\omega t$ or $sin\omega t=x/A$
$v=dx/dt=A\omega cos\omega t$ or $cos\omega t=v/A\omega$
Thus, using $si{n}^2+co{s}^2=1$, $x^2/A^2+x^2/A^2{\omega }^2=1$, which gives the equation of ellipse.
Thus statement 1 is correct. Also, statement 2 is correct but it doesn't explain the reason.