A mass $m = 8\,kg$ is attahced to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is $200\,N/m$. The mass $m$ is then released and begins to undergo small oscillations. The maximum velocity of the mass will be ..... $m/s$ $(g = 10\,m/s^2)$
A mass $m = 8\,kg$ is attahced to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is $200\,N/m$. The mass $m$ is then released and begins to undergo small oscillations. The maximum velocity of the mass will be ..... $m/s$ $(g = 10\,m/s^2)$
- A
$1$
- B
$2$
- C
$4$
- D
$5$
Similar Questions
In figure $(A),$ mass ' $2 m$ ' is fixed on mass ' $m$ ' which is attached to two springs of spring constant $k$. In figure $(B),$ mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2 k$ '. If mass ' $m$ ' in $(A)$ and $(B)$ are displaced by distance ' $x$ ' horizontally and then released, then time period $T_{1}$ and $T_{2}$ corresponding to $(A)$ and $(B)$ respectively follow the relation.
In figure $(A),$ mass ' $2 m$ ' is fixed on mass ' $m$ ' which is attached to two springs of spring constant $k$. In figure $(B),$ mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2 k$ '. If mass ' $m$ ' in $(A)$ and $(B)$ are displaced by distance ' $x$ ' horizontally and then released, then time period $T_{1}$ and $T_{2}$ corresponding to $(A)$ and $(B)$ respectively follow the relation.
- [JEE MAIN 2022]
In the figure, ${S_1}$ and ${S_2}$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed, the frequency will become
In the figure, ${S_1}$ and ${S_2}$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed, the frequency will become
A mass m oscillates with simple harmonic motion with frequency $f = \frac{\omega }{{2\pi }}$ and amplitude A on a spring with constant $K$ , therefore
A mass m oscillates with simple harmonic motion with frequency $f = \frac{\omega }{{2\pi }}$ and amplitude A on a spring with constant $K$ , therefore
Figure $(a)$ shows a spring of force constant $k$ clamped rigidly at one end and a mass $m$ attached to its free end. A force $F$ applied at the free end stretches the spring. Figure $(b)$ shows the same spring with both ends free and attached to a mass $m$ at etther end. Each end of the spring in Figure $( b )$ is stretched by the same force $F.$
$(a)$ What is the maximum extension of the spring in the two cases?
$(b)$ If the mass in Figure $(a)$ and the two masses in Figure $(b)$ are released, what is the period of oscillation in each case?
Figure $(a)$ shows a spring of force constant $k$ clamped rigidly at one end and a mass $m$ attached to its free end. A force $F$ applied at the free end stretches the spring. Figure $(b)$ shows the same spring with both ends free and attached to a mass $m$ at etther end. Each end of the spring in Figure $( b )$ is stretched by the same force $F.$
$(a)$ What is the maximum extension of the spring in the two cases?
$(b)$ If the mass in Figure $(a)$ and the two masses in Figure $(b)$ are released, what is the period of oscillation in each case?
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 .... $kg$
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 .... $kg$