Two simple pendulums are given: the first has | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The frequency of a simple pendulum is given by $n = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$,which implies $n \propto \frac{1}{\sqrt{L}}$.For the two pen

Vedclass · Accepted Answer

Amplitude of $B$ is smaller than $A$

Vedclass · Answer

(B) The frequency of a simple pendulum is given by $n = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$,which implies $n \propto \frac{1}{\sqrt{L}}$.For the two pendulums,the ratio of frequencies is $\frac{n_1}{n_2} = \sqrt{\frac{L_2}{L_1}} = \sqrt{\frac{L_2}{2L_2}} = \frac{1}{\sqrt{2}}$.Thus,$n_2 = \sqrt{2}n_1$,which means $n_2 > n_1$.The vibrational energy of a simple harmonic oscillator is $E = 2\pi^2 m n^2 a^2$,where $a$ is the amplitude.Since $E_1 = E_2$,$m_1 = m_2$,and $n_2 > n_1$,we have $n_1^2 a_1^2 = n_2^2 a_2^2$.Therefore,$\frac{a_1^2}{a_2^2} = \frac{n_2^2}{n_1^2} = 2$,which implies $a_1 = \sqrt{2}a_2$.Since $a_1 > a_2$,the amplitude of pendulum $B$ is smaller than that of pendulum $A$.

Two simple pendulums are given: the first has a bob of mass $M_1$ and length $L_1$,and the second has a bob of mass $M_2$ and length $L_2$. Given $M_1 = M_2$ and $L_1 = 2L_2$. If the vibrational energy of both is the same,which of the following statements is correct?

Similar Questions

The time period of a simple pendulum is $T$. When the length is increased by $10 \ cm$, its period is $T_1$. When the length is decreased by $10 \ cm$, its period is $T_2$. Then, the relation between $T, T_1$, and $T_2$ is

$A$ hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will

$A$ simple pendulum is taken to a place where its distance from the Earth's surface is equal to the radius of the Earth. Calculate the time period of small oscillations if the length of the string is $4.0 \ m$. (Take $g = \pi^2 \ m/s^2$ at the surface of the Earth.) (in $s$)

$A$ chimpanzee swinging on a swing in a sitting position,stands up suddenly,the time period will

Vedclass Test Series

Exam Paper Generator

Online Exam Module