For a simple harmonic motion in a mass-spring | vedclass

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

Question

(B) The angular frequency $\omega$ of a mass-spring system is given by the formula $\omega = \sqrt{\frac{k}{m}}$,where $k$ is the spring constant and

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}}$

Vedclass · Answer

(B) The angular frequency $\omega$ of a mass-spring system is given by the formula $\omega = \sqrt{\frac{k}{m}}$,where $k$ is the spring constant and $m$ is the mass of the block.Given that the spring constant $k$ remains the same for both cases,we have:$\omega_1 = \sqrt{\frac{k}{m_1}}$ and $\omega_2 = \sqrt{\frac{k}{m_2}}$Taking the ratio of $\omega_2$ to $\omega_1$:$\frac{\omega_2}{\omega_1} = \frac{\sqrt{k/m_2}}{\sqrt{k/m_1}} = \sqrt{\frac{m_1}{m_2}}$Substituting the given values $m_1 = 1\,kg$ and $m_2 = 2\,kg$:$\frac{\omega_2}{\omega_1} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$

For a simple harmonic motion in a mass-spring system shown,the surface is frictionless. When the mass of the block is $1\,kg$,the angular frequency is $\omega_1$. When the mass of the block is $2\,kg$,the angular frequency is $\omega_2$. The ratio $\omega_2 / \omega_1$ is

Similar Questions

$A$ block of mass $m$ is at rest on another block of the same mass as shown in the figure. The lower block is attached to a spring. What is the maximum amplitude of motion such that both blocks remain in contact?

$A$ block of mass $m$ hangs from three springs having the same spring constant $k$. If the mass is slightly displaced downwards,the time period of oscillation will be

The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring is cut to half, the same mass oscillates with frequency $v_2$. The value of $v_2/v_1$ is . . . . . . .

$A$ body of mass $4.9 \, kg$ hangs from a spring and oscillates with a period $0.5 \, s$. On the removal of the body, the spring is shortened by (take $g=10 \, m/s^2, \pi^2=10$)

$A$ body of mass $m$ is suspended to an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

Vedclass Test Series

Exam Paper Generator

Online Exam Module