Question

Which graph (s) can represent the kinetic energy of the spring and mass as a function of distance x?

• A. I only
• B. I and II only
• C. II only
• D. III only
• E. II and III only

Answer 1

The correct option is C II only

Kinetic energy of the spring-mass system is given by

$\frac{1}{2}m{v}^2=\frac{1}{2}m\left(A^2{\omega }^{2}co{s}^2\omega t\right)$

$=\frac{1}{2}m{\omega }^2(A^2-A^{2}si{n}^2\omega t)$

$=\frac{1}{2}m{\omega }^2{A}^2-\frac{1}{2}m{\omega }^2{x}^2$

Hence kinetic energy is maximum at O and equal to zero at $A_1$ and $A_2$.

Correct representation is figure II.