Oscillations of Spring — Prelims Questions

A block of mass $M$ is attached to a spring with spring constant $k$. If the block is pulled to a distance $A$ from its equilibrium position and released, its period of oscillation is $T$. If the mass of the block is doubled to $2M$, what will be the new period of oscillation?

A mass $m$ is attached to a spring and oscillates with a period $T$. If the spring is cut into two equal halves and the same mass $m$ is attached to one of the halves, what will be the new period of oscillation?

A mass $m$ is attached to a spring and oscillates with amplitude $A$. At what displacement from equilibrium is its kinetic energy equal to its potential energy?

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

A mass $m$ is attached to a spring and oscillates horizontally. Its maximum speed is $v_{max}$. What is its speed when its displacement from equilibrium is half of its amplitude ($x = A/2$)?

A mass $m$ is suspended from a spring and oscillates vertically. The period of oscillation is $T$. If this entire setup is taken to the Moon, where the acceleration due to gravity is $g/6$, what will be the new period of oscillation?