Three masses $700g, 500g$, and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3$ seconds, when the $500 \,gm$ mass is also removed, it will oscillate with a period of ...... $s$
Medium
Download our app for free and get started
(b) When mass $700 \,gm$ is removed, the left out mass $(500 + 400)\, gm$ oscillates with a period of $3\, sec$
$3 = t = 2\pi \sqrt {\frac{{(500 + 400)}}{k}} $…...$(i)$
When $500 \,gm$ mass is also removed, the left out mass is $400\, gm.$
$t' = 2\pi \sqrt {\frac{{400}}{k}} $…..$(ii)$
==> $\frac{3}{{t'}} = \sqrt {\frac{{900}}{{400}}} $ ==> $t' = 2\sec $
$3 = t = 2\pi \sqrt {\frac{{(500 + 400)}}{k}} $…...$(i)$
When $500 \,gm$ mass is also removed, the left out mass is $400\, gm.$
$t' = 2\pi \sqrt {\frac{{400}}{k}} $…..$(ii)$
==> $\frac{3}{{t'}} = \sqrt {\frac{{900}}{{400}}} $ ==> $t' = 2\sec $
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
- 1If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is:View Solution
- 2A particle executes $S.H.M.$ with a period of $6$ second and amplitude of $3\, cm$. Its maximum speed in $cm/sec$ isView Solution
- 3In the reported figure, two bodies $A$ and $B$ of masses $200\, {g}$ and $800\, {g}$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be $.....\,{rad} / {s}$ when ${k}=20 \,{N} / {m} .$View Solution
- 4At a given point of time the value of displacement of a simple harmonic oscillator is given as $y = A \cos \left(30^{\circ}\right)$. If amplitude is $40\,cm$ and kinetic energy at that time is $200\, J$, the value of force constant is $1.0 \times 10^{ x }\,Nm ^{-1}$. The value of $x$ is ......View Solution
- 5A linear harmonic oscillator of force constant $2 \times {10^6}N/m$ and amplitude $0.01\, m$ has a total mechanical energy of $160$ joules. ItsView Solution
- 6A particle of mass $5 × 10^{-5}\ kg$ is placed at lowest point of smooth parabola $x^2 = 40y$ ( $x$ and $y$ in $m$ ). If it is displaced slightly such that it is constrained to move along parabola, angular frequency of oscillation (in $rad/s$) will be approximately:-View Solution
- 7A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega $. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first timeView Solution
- 8The kinetic energy of a particle executing $S.H.M.$ is $16\, J$ when it is at its mean position. If the mass of the particle is $0.32 \,kg$, then what is the maximum velocity of the particle ..... $m/s$View Solution
- 9A particle of mass $250\,g$ executes a simple harmonic motion under a periodic force $F =(-25\,x) N$. The particle attains a maximum speed of $4\,m / s$ during its oscillation. The amplitude of the motion is $...........cm$.View Solution
- 10A particle starts oscillating simple harmonically from its equilibrium position then, the ratio of kinetic energy and potential energy of the particle at the time $T/12$ is : ($T =$ time period)View Solution