If displacement x and velocity v are related | vedclass

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

Question

(C) The given equation is $4v^2 = 16 - x^2$.Dividing both sides by $16$,we get $\frac{4v^2}{16} + \frac{x^2}{16} = 1$,which simplifies to $\frac{v^2}{

Vedclass · Accepted Answer

$4\pi$

Vedclass · Answer

(C) The given equation is $4v^2 = 16 - x^2$.Dividing both sides by $16$,we get $\frac{4v^2}{16} + \frac{x^2}{16} = 1$,which simplifies to $\frac{v^2}{4} + \frac{x^2}{16} = 1$.Comparing this with the standard $SHM$ velocity-displacement relation $\frac{v^2}{(A\omega)^2} + \frac{x^2}{A^2} = 1$,we identify:$A^2 = 16 \Rightarrow A = 4$ and $(A\omega)^2 = 4 \Rightarrow A\omega = 2$.Substituting $A = 4$ into $A\omega = 2$,we get $4\omega = 2$,so $\omega = 0.5 	ext{ rad/s}$.The time period $T$ is given by $T = \frac{2\pi}{\omega} = \frac{2\pi}{0.5} = 4\pi 	ext{ s}$.

If displacement $x$ and velocity $v$ are related as $4v^2 = 16 - x^2$ in a $SHM$,then the time period of the given $SHM$ is (consider $SI$ units).

Similar Questions

$A$ particle is performing simple harmonic motion with an amplitude of $0.06 \,m$ and a time period of $3.14 \,s$. The maximum velocity of the particle is . . . . . . $cm/s$.

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 \times 10^{-2} \cos(\pi t) \text{ m}$. The time at which the maximum speed first occurs is (in $\text{ s}$)

The velocity of a particle in simple harmonic motion at displacement $y$ from the mean position is

The maximum velocity of a particle performing simple harmonic motion is $6.28 \text{ cm s}^{-1}$. If the length of its path is $8 \text{ cm}$, then what is its period (in $\text{ s}$)?

$A$ particle is executing simple harmonic motion. If the force acting on the particle at a position is $86.6 \%$ of the maximum force on it, then the ratio of its velocity at that point and its maximum velocity is

Vedclass Test Series

Exam Paper Generator

Online Exam Module