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]$

Column-$I$	Column-$II$
$(a)$ $T^2 \to l$	$(i)$ Linear
$(b)$ $T^2 \to g$	$(ii)$ Parabolic
$(c)$ $T \to l$	$(iii)$ Hyperbolic

$A$ 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 acceleration due to gravity on the surface of the moon is $1.7 \; m s^{-2}$. What is the time period of a simple pendulum on the surface of the moon if its time period (in $s$) on the surface of the earth is $3.5 \; s$? ($g$ on the surface of the earth is $9.8 \; m s^{-2}$)

Identify the correct statement.

$A$ plate oscillates with a time period $T$. If another plate is suddenly placed on the first plate,what happens to the time period?

The ratio of frequencies of two oscillating pendulums are $3: 2$. Their lengths are in the ratio:

In the following table, the relation of the graph in column-$I$ and the shape of the graph in column-$II$ is shown. Match them appropriately.
Column-$I$ Column-$II$
$(a)$ $T^2 \to l$ $(i)$ Linear
$(b)$ $T^2 \to g$ $(ii)$ Parabolic
$(c)$ $T \to l$ $(iii)$ Hyperbolic

Vedclass Test Series

Exam Paper Generator

Online Exam Module