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 ..... $m/s$ $(g = 10\,m/s^2)$
Medium
Download our app for free and get started
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{K}}}$
or $\omega=\sqrt{\frac{\mathrm{K}}{\mathrm{M}}}=5 \mathrm{rad} / \mathrm{sec}$
and $A=m g / K=2 / 5 \mathrm{m}$
$\mathrm{v}_{\max }=\omega \mathrm{A}=2 \mathrm{m} / \mathrm{s}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A 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 .... $kg$View Solution
- 2There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum isView Solution
- 3View SolutionWhich of the following equation does not represent a simple harmonic motion
- 4A simple pendulum suspended from the ceiling of a stationary lift has period $T_0$. When the lift descends at steady speed, the period is $T_1$, and when it descends with constant downward acceleration, the period is $T_2$. Which one of the following is true?View Solution
- 5A particle executes $S.H.M.$ with amplitude $'a'$ and time period $V$. The displacement of the particle when its speed is half of maximum speed is $\frac{\sqrt{ x } a }{2} .$ The value of $x$ is $\ldots \ldots \ldots$View Solution
- 6A pendulum with time period of $1\, s$ is losing energy due to damping. At certain time its energy is $45\, J$. If after completing $15\,oscillations$ , its energy has become $15\, J$, its damping constant (in $s^{-1}$ ) isView Solution
- 7A pendulum suspended from the ceiling of a train oscillates with a time period $2$ $second$ , when the train is accelerating at $10\,ms^{-2}$. What will be its time period when the train retards at $10\,ms^{-2}$ ? .... $s$View Solution
- 8A simple pendulum oscillates in air with time period $T$ and amplitude $A$. As the time passesView Solution
- 9View SolutionThe velocity of simple pendulum is maximum at
- 10A pendulum is suspended by a string of length $250\,cm$. The mass of the bob of the pendulum is $200\,g$. The bob is pulled aside until the string is at $60^{\circ}$ with vertical as shown in the figure. After releasing the bob. the maximum velocity attained by the bob will be________ $ms ^{-1}$. (if $g=10\,m / s ^{2}$ )View Solution
