What is spring constant of spring ? Write its unit and dimensional formula.

The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If length of spring is cut to one third then the same mass oscillates with frequency $v_2$, then

The time period of simple harmonic motion of mass $\mathrm{M}$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$, where the value of $\alpha$ is____.

A steady force of $120\ N$ is required to push a boat of mass $700\ kg$ through water at a constant speed of $1\ m/s$ . If the boat is fastened by a spring and held at $2\ m$ from the equilibrium position by a force of $450\ N$ , find the angular frequency of damped $SHM$  ..... $rad/s$ 

A mass of $0.2\,kg$ is attached to the lower end of a massless spring of force-constant $200\, N/m,$ the upper end of which is fixed to a rigid support. Which of the following statements is/are true ?

The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be