A particle is executing a simple harmonic mot | vedclass

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

Question

(A) For a particle in simple harmonic motion with amplitude $A$ and angular frequency $\omega$:Maximum acceleration is given by $\alpha = A\omega^2$.M

Vedclass · Accepted Answer

$\frac{2\pi \beta}{\alpha}$

Vedclass · Answer

(A) For a particle in simple harmonic motion with amplitude $A$ and angular frequency $\omega$:Maximum acceleration is given by $\alpha = A\omega^2$.Maximum velocity is given by $\beta = A\omega$.Dividing the two equations: $\frac{\alpha}{\beta} = \frac{A\omega^2}{A\omega} = \omega$.Therefore,$\omega = \frac{\alpha}{\beta}$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.Substituting the value of $\omega$: $T = \frac{2\pi}{(\alpha / \beta)} = \frac{2\pi \beta}{\alpha}$.

$A$ particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then,its time period of vibration will be

Similar Questions

$A$ wooden cube of side $10 \ cm$ floats at the interface between water and oil with its lower surface $3 \ cm$ below the interface. If the density of oil is $0.9 \ g \ cm^{-3}$, the mass of the wooden cube is (in $g$)

The equations of the normals at the ends of the latus rectum of the parabola $y^2 = 4ax$ are given by

The number of ways that $8$ beads of different colours can be strung as a necklace is

Which element among the alkaline earth metals primarily forms covalent compounds?

The ratio of the centripetal accelerations of the electron in two successive orbits of hydrogen is $81: 16$. Due to a transition between these two states,the angular momentum of the electron changes by ($h$ - Planck's constant).

Vedclass Test Series

Exam Paper Generator

Online Exam Module