A pendulum is executing simple harmonic motio | vedclass

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

Question

(A) The maximum kinetic energy of a simple pendulum at its lowest point is equal to the potential energy at its maximum angular displacement $	heta$.

Vedclass · Accepted Answer

$K_2 = 2K_1$

Vedclass · Answer

(A) The maximum kinetic energy of a simple pendulum at its lowest point is equal to the potential energy at its maximum angular displacement $	heta$.The potential energy $U$ at an angular displacement $	heta$ is given by $U = mg\ell(1 - \cos 	heta)$,where $m$ is the mass,$g$ is the acceleration due to gravity,and $\ell$ is the length of the pendulum.For the first case,the maximum kinetic energy is $K_1 = mg\ell(1 - \cos 	heta)$.In the second case,the length is doubled $(\ell' = 2\ell)$ and the angular amplitude $	heta$ remains the same. The new maximum kinetic energy is $K_2 = mg(2\ell)(1 - \cos 	heta)$.Comparing the two expressions,we get $K_2 = 2 	imes [mg\ell(1 - \cos 	heta)] = 2K_1$.

$A$ pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_1$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same angular amplitude as in the first case,its maximum kinetic energy is $K_2$,then:

Similar Questions

The length of a seconds pendulum on the surface of the Earth is $1\, m$. The length of a seconds pendulum on the surface of the Moon,where $g$ is $1/6$th the value of $g$ on the surface of the Earth,is:

Two simple pendulums of lengths $1.44 \, m$ and $1 \, m$ start swinging together. After how many vibrations will they again start swinging together?

The path length of oscillation of a simple pendulum of length $1 \,m$ is $16 \,cm$. Its maximum velocity is (Take $g = \pi^2 \,m/s^2$).

Choose the correct length $(L)$ versus square of time period $(T^2)$ graph for a simple pendulum executing simple harmonic motion.

The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water,then the new time period is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module