Spring-Mass System — Prelims Questions

A block of mass $M$ is attached to a spring of spring constant $k$. The system oscillates with a time period $T$. If the mass of the block is doubled and the spring is cut into two equal halves, what will be the new time period of oscillation?

A mass $m$ is suspended from a spring of spring constant $k$. It oscillates with a time period $T$. If the mass is replaced by $4m$, what will be the new time period?

Two springs of spring constants $k_1$ and $k_2$ are connected in series. A mass $m$ is attached to the combination. What is the equivalent spring constant of the system?

A mass $m$ attached to a spring oscillates with an amplitude $A$. What is the ratio of its kinetic energy to its potential energy when its displacement from equilibrium is $A/2$?

A spring of length $L$ and spring constant $k$ is cut into two pieces of lengths $L/3$ and $2L/3$. If a mass $m$ is attached to the longer piece, what will be the time period of oscillation?

A mass $m$ is attached to two springs in parallel, with spring constants $k_1$ and $k_2$. What is the angular frequency of oscillation?