Two masses $m_1$ and $m_2$ are supended together by a massless spring of constant $k$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system; the amplitude of vibration is
Medium
Download our app for free and get started
In equillibrium $F=\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{g}$
By removing mass $m_1$
$F^{\prime}=\mathrm{m}_{2} \mathrm{g}$
$F_{\mathrm{r}}=F^{\prime}-F=\mathrm{m}_{2} \mathrm{g}-\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right)$
$\mathrm{kx}=\mathrm{m}_{1} \mathrm{g} \Rightarrow \mathrm{x}=\frac{\mathrm{m}_{1} \mathrm{g}}{\mathrm{k}}$
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
- 1The angular velocity and the amplitude of a simple pendulum is $'\omega '$ and $'A'$ respectively. At a displacement $x$ from the mean position its kinetic energy is $'T'$ and potnetial energy is $'V'$. Then the ratio $\frac{V}{T}$ isView Solution
- 2A simple pendulum of length $l$ and mass $m$ of the bob is suspended in a car that is travelling with a constant speed $v$ around a circular path of radius $R$. If the pendulum undergoes oscillations with small amplitude about its equilibrium position, the frequency of its oscillations will beView Solution
- 3View SolutionA particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true
- 4The displacement of a particle moving in $S.H.M.$ at any instant is given by $y = a\sin \omega t$. The acceleration after time $t = \frac{T}{4}$ is (where $T$ is the time period)View Solution
- 5For a particle executing simple harmonic motion, the kinetic energy $K$ is given by $K = {K_o}{\cos ^2}\omega t$. The maximum value of potential energy isView Solution
- 6Two particles are executing $SHM$ of the same amplitude $A$ and frequency $\omega $ along the $x-$ axis. Their mean position is separated by $X_0$ (where $X_0 > A$ ). If maximum separation between them is $X_0 + 2A$ , then the phase difference between their motion isView Solution
- 7View SolutionFive identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations (i), (ii) and (iii) are in the ratio
- 8A $5\, kg$ collar is attached to a spring of spring constant $500\, Nm^{-1}$. It slides without friction over a horizontal rod. The collar is displaced from its equillibrium position by $10\, cm$ and released. The time period of oscillation isView Solution
- 9Assuming all pulleys, springs and string massless. Consider all surface smooth. Choose the correct statement $(s)$View Solution
- 10A block $P$ of mass $m$ is placed on a smooth horizontal surface. A block $Q$ of same mass is placed over the block $P$ and the coefficient of static friction between them is ${\mu _S}$. A spring of spring constant $K$ is attached to block $Q$. The blocks are displaced together to a distance $A$ and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block isView Solution
