A mass m_1 connected to a horizontal spring p | vedclass

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

Question

(A) At the mean position,the potential energy is zero and the kinetic energy is maximum. The velocity $v$ of mass $m_1$ at the mean position is $v = A

Vedclass · Accepted Answer

$\left[\frac{m_1}{m_1 + m_2}\right]^{\frac{1}{2}}$

Vedclass · Answer

(A) At the mean position,the potential energy is zero and the kinetic energy is maximum. The velocity $v$ of mass $m_1$ at the mean position is $v = A\omega = A\sqrt{\frac{k}{m_1}}$.When mass $m_2$ is placed on $m_1$,the momentum is conserved because the spring force is zero at the mean position. Let $v'$ be the new velocity:$m_1 v = (m_1 + m_2) v'$$v' = \frac{m_1 v}{m_1 + m_2} = \frac{m_1 A \sqrt{k/m_1}}{m_1 + m_2} = A \sqrt{\frac{k m_1}{(m_1 + m_2)^2}}$.The new energy of the system is $E' = \frac{1}{2} k A_1^2 = \frac{1}{2} (m_1 + m_2) (v')^2$.Substituting $v'$:$\frac{1}{2} k A_1^2 = \frac{1}{2} (m_1 + m_2) \left( A^2 \frac{k m_1}{(m_1 + m_2)^2} \right)$.$A_1^2 = A^2 \frac{m_1}{m_1 + m_2}$.Therefore,$\frac{A_1}{A} = \sqrt{\frac{m_1}{m_1 + m_2}}$.

$A$ 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:

Similar Questions

$A$ mass $M$,attached to a horizontal spring,executes $S.H.M.$ with amplitude $A_1$. When the mass $M$ passes through its mean position,a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\frac{A_1}{A_2}$ is

Springs of spring constants $K, 2K, 4K, 8K, \dots$ are connected in series. $A$ mass of $40 \, g$ is attached to the lower end of the last spring and the system is allowed to vibrate. What is the time period of oscillation in seconds? (Given $K = 2 \, N/cm$)

Frequency of a particle performing $S.H.M.$ is $10 \ Hz$. The particle is suspended from a vertical spring. At the highest point of its oscillation,the spring is unstretched. The maximum speed of the particle is $(g = 10 \ m/s^2)$.

$A$ mass hangs from a spring and oscillates vertically. The top end of the spring is attached to the top of a box,and the box is placed on a scale,as shown in the figure. The reading on the scale is largest when the mass is

Vedclass Test Series

Exam Paper Generator

Online Exam Module