Two bodies A and B of equal masses are suspen | vedclass

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

Question

(D) The maximum velocity of an object in simple harmonic motion is given by $v_{max} = A \omega$,where $A$ is the amplitude and $\omega$ is the angula

Vedclass · Accepted Answer

$\sqrt{\frac{k_2}{k_1}}$

Vedclass · Answer

(D) The maximum velocity of an object in simple harmonic motion is given by $v_{max} = A \omega$,where $A$ is the amplitude and $\omega$ is the angular frequency.Given that the masses are equal $(m_1 = m_2 = m)$,the angular frequencies are $\omega_1 = \sqrt{\frac{k_1}{m}}$ and $\omega_2 = \sqrt{\frac{k_2}{m}}$.Since the maximum velocities are equal,we have $A_1 \omega_1 = A_2 \omega_2$.Rearranging for the ratio of amplitudes,we get $\frac{A_1}{A_2} = \frac{\omega_2}{\omega_1}$.Substituting the expressions for $\omega_1$ and $\omega_2$,we get $\frac{A_1}{A_2} = \frac{\sqrt{k_2/m}}{\sqrt{k_1/m}} = \sqrt{\frac{k_2}{k_1}}$.Thus,the ratio of the amplitudes is $\sqrt{\frac{k_2}{k_1}}$.

Two bodies $A$ and $B$ of equal masses are suspended from two separate springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate such that their maximum velocities are equal,the ratio of the amplitudes of oscillation of $A$ and $B$ will be

Similar Questions

$A$ particle connected to the end of a spring executes $S$.$H$.$M$. with period $T_1$. While the corresponding period for another spring is $T_2$. If the period of oscillation with two springs in series is $T$,then

$A$ bar of mass $m$ is suspended horizontally on two vertical springs of spring constant $k$ and $3k$. The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar (Neglect mass of springs and friction everywhere).

Two springs of spring constants $k_1$ and $k_2$ are connected to a mass $m$ as shown in the figure. Under negligible friction, if the mass is displaced by a small amount $x$ from its equilibrium position and released, the period of oscillation is

$A$ mass $m_1$ connected to a horizontal spring performs $S.H.M.$ with amplitude $A$. While mass $m_1$ is passing through the mean position,another mass $m_2$ is placed on it so that both the masses move together with amplitude $A_1$. The ratio of $\frac{A_1}{A}$ is:

Two springs of force constants $K$ and $2K$ are connected to a mass $m$ as shown in the figure. The frequency of oscillation of the mass is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module