Two simple pendulum first of bob mass $M_1$ and length $L_1$ second of bob mass $M_2$ and length $L_2$. $M_1 = M_2$ and $L_1 = 2L_2$. If these vibrational energy of both is same. Then which is correct
Medium
Download our app for free and get started
(b) $n = \frac{1}{{2\pi }}\sqrt {\frac{g}{l}} $==> $n \propto \frac{1}{{\sqrt l }}$==> $\frac{{{n_1}}}{{{n_2}}} = \sqrt {\frac{{{l_2}}}{{{l_1}}}} = \sqrt {\frac{{{L_2}}}{{2{L_2}}}} $
==> $\frac{{{n_1}}}{{{n_2}}} = \frac{1}{{\sqrt 2 }}$==> ${n_2} = \sqrt 2 \,{n_1}$ ==> ${n_2} > {n_1}$
Energy $E = \frac{1}{2}m{\omega ^2}{a^2} = 2{\pi ^2}m{n^2}{a^2}$
==>$\frac{{a_1^2}}{{a_2^2}} = \frac{{{m_2}n_2^2}}{{{m_1}n_1^2}}$ ( $E$ is same)
Given ${n_2} > {n_1}$ and ${m_1} = {m_2}$ ==> ${a_1} > {a_2}$
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
- 1View SolutionIf a body is released into a tunnel dug across the diameter of earth, it executes simple harmonic motion with time period
- 2A particle of mass $m$ is dropped from a height $R$ equal to the radius of the earth above the tunnel dug through the earth as shown in the figure. Hence the correct statement isView Solution
- 3The amplitude of a particle executing $SHM$ is $4 \,cm$. At the mean position the speed of the particle is $16\, cm/sec$. The distance of the particle from the mean position at which the speed of the particle becomes $8\sqrt 3 \,cm/s,$ will be .... $cm$View Solution
- 4The graphs in figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graphs best represents the relationship obtained when $y$ is The total energy of the systemView Solution
- 5A block of mass $m$ is having two similar rubber ribbons attached to it as shown in the figure. The force constant of each rubber ribbon is $K$ and surface is frictionless. The block is displaced from mean position by $x\,cm$ and released. At the mean position the ribbons are underformed. Vibration period isView Solution
- 6Speed $v$ of a particle moving along a straight line, when it is at a distance $x$ from a fixed point on the line is given by $v^2 = 108 - 9x^2$ (all quantities in $S.I.$ unit). ThenView Solution
- 7A particle is placed at the lowest point of a smooth wire frame in the shape of a parabola, lying in the vertical $xy-$ plane having equation $x^2 = 5y$ $(x, y$ are in meter). After slight displacement, the particle is set free. Find angular frequency of oscillation.....$rad/s$ (in $rad/sec$ ) (take $g = 10\ m/s^2$ )View Solution
- 8A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration $a$, then the time period is given by $T = 2\pi \sqrt {\frac{l}{{g'}}} $, where $g'$ is equal toView Solution
- 9A particle moving along the $X-$axis executes simple harmonic motion, then the force acting on it is given byView Solution
Where $A$ and $K$ are positive constants
- 10The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $\pi $ results in the displacement of the particle alongView Solution