A simple pendulum of length 'l' and a bob of | vedclass

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

Question

(B) The tension $T$ in the string of a simple pendulum at any angle $	heta$ is given by the radial force balance equation:$T = mg \cos 	heta + \frac

Vedclass · Accepted Answer

$mg\left[1+\left(\frac{A}{l}\right)^2\right]$

Vedclass · Answer

(B) The tension $T$ in the string of a simple pendulum at any angle $	heta$ is given by the radial force balance equation:$T = mg \cos 	heta + \frac{mv^2}{l}$For small oscillations,$\cos 	heta \approx 1$ and the velocity $v$ is maximum at the mean position $(	heta = 0)$.Thus,the maximum tension $T_{\max}$ occurs at the mean position:$T_{\max} = mg + \frac{mv_{\max}^2}{l}$For a simple pendulum,the angular frequency is $\omega = \sqrt{\frac{g}{l}}$.The maximum velocity in $S$.$H$.$M$. is $v_{\max} = A\omega$.Substituting $v_{\max}$ into the tension equation:$T_{\max} = mg + \frac{m(A\omega)^2}{l}$$T_{\max} = mg + \frac{m A^2 \omega^2}{l}$Since $\omega^2 = \frac{g}{l}$,we get:$T_{\max} = mg + \frac{m A^2 (g/l)}{l}$$T_{\max} = mg + \frac{m A^2 g}{l^2}$$T_{\max} = mg \left[1 + \left(\frac{A}{l}ight)^2ight]$

$A$ simple pendulum of length '$l$' and a bob of mass '$m$' is executing $S$.$H$.$M$. of small amplitude '$A$'. The maximum tension in the string will be ($g=$ acceleration due to gravity).

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

The angular velocity and the amplitude of a simple pendulum are $\omega$ and $A$ respectively. At a displacement $x$ from the mean position,its kinetic energy is $T$ and potential energy is $V$. Then the ratio $\frac{V}{T}$ is

The ratio of the period of oscillation of a conical pendulum to that of a simple pendulum is: (Assume the strings are of the same length in both cases and $\theta$ is the angle made by the string with the vertical in the case of the conical pendulum.)

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$,is given by

$A$ pendulum clock is running slow. To correct its time,we should

Vedclass Test Series

Exam Paper Generator

Online Exam Module