$A$ 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 $\pi/4 \ s$ is .... $kg$.

$A$ particle of mass $0.50 \ kg$ executes simple harmonic motion under force $F = -50 \ (N/m) x$. The time period of oscillation is $\frac{x}{35} \ s$. The value of $x$ is . . . . . (Given $\pi = \frac{22}{7}$)

$A$ mass $m$ performs oscillations of period $T$ when suspended by a spring of force constant $K$. If the spring is cut into two equal parts and arranged in parallel,and the same mass $m$ is oscillated by them,then the new time period will be:

$A$ $1 \, kg$ block attached to a spring vibrates with a frequency of $1 \, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8 \, kg$ block placed on the same table. The frequency of vibration of the $8 \, kg$ block is ..... $Hz$.

Two small bodies of mass $2 \, kg$ each are attached to each other using a thread of length $10 \, cm$,and hang on a spring whose force constant is $200 \, N/m$,as shown in the figure. We burn the thread. What is the distance between the two bodies when the top body first arrives at its highest position? (Take $\pi^2 = 10$)

As shown in the figure,two blocks of masses $m_1$ and $m_2$ are connected to a spring of force constant $k$. The blocks are slightly displaced in opposite directions to $x_1$ and $x_2$ distances and released. If the system executes simple harmonic motion,then the angular frequency of oscillation of the system $(\omega)$ is: