If the speed v of the bob in a simple pendulu | vedclass

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

Question

(A) For a simple pendulum undergoing simple harmonic motion,the displacement $x$ is given by $x = A \sin(\omega t)$.The velocity is $v = \frac{dx}{dt}

Vedclass · Accepted Answer

$I$

Vedclass · Answer

(A) For a simple pendulum undergoing simple harmonic motion,the displacement $x$ is given by $x = A \sin(\omega t)$.The velocity is $v = \frac{dx}{dt} = A\omega \cos(\omega t)$.The tangential acceleration is $a = \frac{dv}{dt} = -A\omega^2 \sin(\omega t)$.From these equations,we have:$\frac{v}{A\omega} = \cos(\omega t)$ and $\frac{a}{-A\omega^2} = \sin(\omega t)$.Using the identity $\sin^2(	heta) + \cos^2(	heta) = 1$,we get:$\left(\frac{v}{A\omega}ight)^2 + \left(\frac{a}{-A\omega^2}ight)^2 = 1$$\frac{v^2}{A^2\omega^2} + \frac{a^2}{A^2\omega^4} = 1$This is the equation of an ellipse in the $v-a$ plane,where $v$ is on the horizontal axis and $a$ is on the vertical axis. Thus,the correct graph is $I$.

If the speed $v$ of the bob in a simple pendulum is plotted against the tangential acceleration $a$,the correct graph will be represented by

Similar Questions

If a body dropped freely from a height of $20 \,m$ reaches the surface of a planet with a velocity of $31.4 \,ms^{-1}$, then the length of a simple pendulum that ticks seconds on the planet is (in $\,m$)

$A$ simple pendulum oscillates freely between points $A$ and $B$. We now put a peg (nail) at the point $C$ as shown in the figure. As the pendulum moves from $A$ to the right,the string will bend at $C$ and the pendulum will go to its extreme point $D$. Ignoring friction,the point $D$

The ratio of frequencies of oscillations of two simple pendulums is $3: 4$,then their lengths are in the ratio

The period of a simple pendulum is measured as $T$ in a stationary lift. If the lift moves upwards with an acceleration of $5g$,the new period will be:

If the length of a simple pendulum is increased by $300\%$,then the time period will be increased by ..... $\%$

Vedclass Test Series

Exam Paper Generator

Online Exam Module