Question

A mass $m$, suspended vertically by a massless ideal spring with spring constant $k,$ is at rest. The mass is displaced upward by a height $h$. When released, the kinetic energy of the mass will be proportional to
(Neglecting air resistance)

• A. only h
• B. only $h^2$
• C. m
• D. a linear combination of terms involving h and $h^2$ ?
• E. k

Answer 1

Answer: (D)

A mass suspended by amassless spring is given in figure

Mass $m$ is displaced by height $h$, then potential energy of spring and change in gravitational potential energy due to height
$U_{\text{spring }}=\frac{1}{2}k{x}^2=\frac{1}{2}k{h}^2$
and $U_{\text{gravitation }}=mgh$
If the system is released, then both the energies converted into kinetic energy.
Hence, $KE=\frac{1}{2}k{h}^2+mgh$
So, kinetic energy of mass is a linear combination of terms $(\frac{1}{2}k{h}^2$ and $mgh)$ involving $h$ and $h^2$.