Elastic PE — Prelims Questions

A spring is stretched by $2\,\text{cm}$ by a force of $10\,\text{N}$. The energy stored in the spring when it is stretched by $4\,\text{cm}$ will be:

A block of mass $m$ is dropped from a height $h$ onto a vertical spring of spring constant $k$. If the spring is compressed by a maximum distance $x$, what is the relationship between $h$, $x$, $m$, and $k$?

Two springs, one with spring constant $k_1$ and another with $k_2$, are connected in series. An object of mass $m$ is attached to the combination. What is the effective spring constant of the system?

A spring stores $U$ amount of energy when stretched by $x$. If the spring is stretched by $2x$, what is the energy stored?

A $2\,\text{kg}$ mass is attached to a spring of spring constant $200\,\text{N/m}$ and set into oscillation on a frictionless horizontal surface. If the amplitude of oscillation is $0.1\,\text{m}$, what is the maximum speed of the mass?

Which of the following graphs correctly represents the relationship between the elastic potential energy ($U_e$) stored in a spring and its displacement ($x$) from equilibrium?