A mass $M$ is suspended from a light spring. An additional mass m added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period
Medium
Download our app for free and get started
(b) As $mg$ produces extension $x$, hence $k = \frac{{mg}}{x}$
$T = 2\pi \sqrt {\frac{{(M + m)}}{k}} = 2\pi \sqrt {\frac{{(M + m)x}}{{mg}}} $
$T = 2\pi \sqrt {\frac{{(M + m)}}{k}} = 2\pi \sqrt {\frac{{(M + m)x}}{{mg}}} $
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
- 1Two particles $P$ and $Q$ start from origin and execute Simple Harmonic Motion along $X-$axis with same amplitude but with periods $3$ seconds and $6$ seconds respectively. The ratio of the velocities of $ P$ and $Q$ when they meet isView Solution
- 2A particle executing a simple harmonic motion of period $2\ s$ . When it is at its extreme displacement from its mean position, it receives an additional energy equal to what it had in its mean position. Due to this , in its subsequent motion,View Solution
- 3In an elevator, a spring clock of time period $T_S$ (mass attached to a spring) and a pendulum clock of time period $T_P$ are kept. If the elevator accelerates upwardsView Solution
- 4A mass $m$ attached to free end of a spring executes SHM with a period of $1\; s$. If the mass is increased by $3\; kg$ the period of oscillation increases by one second, the value of mass $m$ is $..............kg$.View Solution
- 5A spring block system in horizontal oscillation has a time-period $T$. Now the spring is cut into four equal parts and the block is re-connected with one of the parts. The new time period of vertical oscillation will beView Solution
- 6For a particle showing motion under the force $F=-5(x-2)$, the motion is ...........View Solution
- 7A flat horizontal board moves up and down under $S.H.M.$ vertically with amplitude $A$. The shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is ..........View Solution
- 8A simple pendulum is attached to a block which slides without friction down an inclined plane $A B C$ having an angle of inclination $\alpha$ as shown below. While the block is sliding down the pendulum oscillates in such a way that at its mean position the direction of the string isView Solution
- 9$Assertion :$ For a particle performing $SHM$, its speed decreases as it goes away from the mean position.View Solution
$Reason :$ In $SHM$, the acceleration is always opposite to the velocity of the particle. - 10Two simple pendulums of lengths $1.44 \,m$ and $1\, m$ start swinging together. After how many vibrations will they again start swinging togetherView Solution