Three mass and string system is in equilibrium. When $700\,gm$ mass is removed, then the system oscillates with a period of $3\,seconds$ . When the $500\,gm$ mass is also removed, then what will be new time period for system ..... $\sec$
Medium
Download our app for free and get started
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}} \Rightarrow \mathrm{T} \propto \sqrt{\mathrm{m}}$
$\therefore \frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}=\sqrt{\frac{\mathrm{m}_{2}}{\mathrm{m}_{1}}}=\sqrt{\frac{400}{900}}$
$\Rightarrow \frac{\mathrm{T}_{2}}{3}=\frac{2}{3} \Rightarrow \mathrm{T}_{2}=2 \mathrm{s}$
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 mass at the end of a spring executes harmonic motion about an equilibrium position with an amplitude $A.$ Its speed as it passes through the equilibrium position is $V.$ If extended $2A$ and released, the speed of the mass passing through the equilibrium position will beView Solution
- 2Which one of the following equations of motion represents simple harmonic motion ?View Solution
Where $k,k_0,k_1$ and $a$ are all positive
- 3Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing $S.H.M.$ isView Solution
- 4A particle is vibrating in a simple harmonic motion with an amplitude of $4\, cm.$ At what displacement from the equilibrium position, is its energy half potential and half kineticView Solution
- 5Let $T_1$ and $T_2$ be the time periods of two springs $A$ and $B$ when a mass $m$ is suspended from them separately. Now both the springs are connected in parallel and same mass $m$ is suspended with them. Now let $T$ be the time period in this position. ThenView Solution
- 6View SolutionThe total energy of a particle, executing simple harmonic motion is
- 7If a simple pendulum is taken to place where g decreases by $2\%$, then the time periodView Solution
- 8The equation of motion of a particle is $\frac{{{d^2}y}}{{d{t^2}}} + Ky = 0$, where $K$ is positive constant. The time period of the motion is given byView Solution
- 9View SolutionA second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket
- 10Four harmonic waves of equal frequencies and equal intensities $I_0$ have phase angles $0, \pi / 3,2 \pi / 3$ and $\pi$. When they are superposed, the intensity of the resulting wave is $nI _0$. The value of $n$ isView Solution