Two simple pendulums whose lengths are $100 cm$ and $121 cm$ are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum, will the two be in phase again
Medium
Download our app for free and get started
(b) Let ${T_1}$ and ${T_2}$ are the time period of the two pendulums ${T_1} = 2\pi \sqrt {\frac{{100}}{g}} $ and ${T_2} = 2\pi \sqrt {\frac{{121}}{g}} $
$({T_1} < {T_2}$ because ${l_1} < {l_2})$.
Let at $t = 0$, they start swinging together. Since their time periods are different, the swinging will not be in unision always.
$({T_1} < {T_2}$ because ${l_1} < {l_2})$.
Let at $t = 0$, they start swinging together. Since their time periods are different, the swinging will not be in unision always.
Only when number of completed oscillation differs by an integer, the two pendulum will again begin to swing together.
Let longer length pendulum complete $n$ oscillation and shorter length pendulum complete $(n+1)$ oscillation, for the unision swinging, then $(n + 1){T_1} = n{T_2}$
$(n + 1) \times 2\pi \sqrt {\frac{{100}}{g}} = n \times 2\pi \sqrt {\frac{{121}}{g}} $$ \Rightarrow n = 10$
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
- 1As per given figures, two springs of spring constants $K$ and $2\,K$ are connected to mass $m$. If the period of oscillation in figure $(a)$ is $3 s$, then the period of oscillation in figure $(b)$ will be $\sqrt{ x }$ s. The value of $x$ is$.........$View Solution
- 2Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to $A$ and $T,$ respectively. At time $t=0$ one particle has displacement $A$ while the other one has displacement $\frac {-A}{2}$ and they are moving towards each other. If they cross each other at time $t,$ then $t$ isView Solution
- 3A body oscillates with a simple harmonic motion having amplitude $0.05\, m .$ At a certain instant, its displacement is $0.01\, m$ and acceleration is $1.0 \,m / s ^{2} .$ The period of oscillation isView Solution
- 4A body of mass $0.01 kg$ executes simple harmonic motion $(S.H.M.)$ about $x = 0$ under the influence of a force shown below : The period of the $S.H.M.$ is .... $s$View Solution
- 5The maximum velocity of a simple harmonic motion represented by $y = 3\sin \,\left( {100\,t + \frac{\pi }{6}} \right)$is given byView Solution
- 6A spring of force constant $k$ is cut into lengths of ratio $1:2:3$ . They are connected in series and the new force constant is $k'$ . Then they are connected in parallel and force constant is $k''$ . Then $k':k''$ isView Solution
- 7The angular frequency of a spring block system is $\omega _0.$ This system is suspended from the ceiling of an elevator moving downwards with a constant speed $v_0.$ The block is at rest relative to the elevator. Lift is suddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement :View Solution
- 8The potential energy of a particle $\left(U_x\right)$ executing $S.H.M$. is given byView Solution
- 9The maximum velocity of a body undergoing $S.H.M$. is $0.2\,m/s$ and its acceleration at $0.1\,m$ from the mean position is $0.4\,m/s^2$. The amplitude of the $S.H.M.$ is .... $m$View Solution
- 10The period of a simple pendulum measured inside a stationary lift is found to be $T$. If the lift starts accelerating upwards with acceleration of $g/3,$ then the time period of the pendulum isView Solution