A block of mass $m$ hangs from three springs having same spring constant $k$. If the mass is slightly displaced downwards, the time period of oscillation will be
$2 \pi \sqrt{\frac{m}{3 k}}$
$2 \pi \sqrt{\frac{3 m}{2 k}}$
$2 \pi \sqrt{\frac{2 m}{3 k}}$
$2 \pi \sqrt{\frac{3 k}{m}}$
A spring with $10$ coils has spring constant $k$. It is exactly cut into two halves, then each of these new springs will have a spring constant
A force of $6.4\ N$ stretches a vertical spring by $0.1\ m$. The mass that must be suspended from the spring so that it oscillates with a time period of $\pi/4\ second$ is .... $kg$
Two springs have spring constants ${K_A}$ and ${K_B}$ and ${K_A} > {K_B}$. The work required to stretch them by same extension will be
A mass attached to a spring is free to oscillate, with angular velocity $\omega,$ in a hortzontal plane without friction or damping. It is pulled to a distance $x_{0}$ and pushed towards the centre with a velocity $v_{ o }$ at time $t=0 .$ Determine the amplitude of the resulting oscillations in terms of the parameters $\omega, x_{0}$ and $v_{ o } .$ [Hint: Start with the equation $x=a \cos (\omega t+\theta)$ and note that the initial velocity is negative.]
A man weighing $60\, kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\, m$ and frequency $\frac{2}{\pi }Hz$. Which of the following statement is correct