Two bodies A and B of equal mass are suspende | vedclass

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

Question

(C) For a body of mass $m$ oscillating with amplitude $A$ and angular frequency $\omega$,the maximum velocity is given by $v_{max} = A\omega$. Given t

Vedclass · Accepted Answer

$\sqrt{\frac{K_1}{K_2}}$

Vedclass · Answer

(C) For a body of mass $m$ oscillating with amplitude $A$ and angular frequency $\omega$,the maximum velocity is given by $v_{max} = A\omega$. Given that the masses are equal $(m_A = m_B = m)$ and the maximum velocities are equal $(v_{max,A} = v_{max,B})$,we have $A_1 \omega_1 = A_2 \omega_2$. Since $\omega = \sqrt{\frac{K}{m}}$,we have $A_1 \sqrt{\frac{K_1}{m}} = A_2 \sqrt{\frac{K_2}{m}}$. Squaring both sides,we get $A_1^2 \frac{K_1}{m} = A_2^2 \frac{K_2}{m}$. Simplifying,$A_1^2 K_1 = A_2^2 K_2$. Therefore,the ratio of the amplitude of $B$ $(A_2)$ to that of $A$ $(A_1)$ is $\frac{A_2}{A_1} = \sqrt{\frac{K_1}{K_2}}$.

Two bodies $A$ and $B$ of equal mass are suspended from two separate massless springs of spring constants $K_1$ and $K_2$ respectively. The two bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitude of $B$ to that of $A$ is

Similar Questions

$A$ block of mass $m$ rests on a platform. The platform is given up and down $SHM$ with an amplitude $d$. What is the maximum frequency so that the block never leaves the platform?

When a mass $M$ is attached to a spring of force constant $k$,the spring stretches by $l$. If the mass oscillates with amplitude $l$,what will be the maximum potential energy stored in the spring?

$A$ mass $m$ is suspended separately by two different springs of spring constant $K_1$ and $K_2$ giving the time periods $t_1$ and $t_2$ respectively. If the same mass $m$ is connected by both springs as shown in the figure,then the time period $t$ is given by the relation:

On a smooth inclined plane,a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has a force constant $K$,the period of oscillation of the body (assuming the springs are massless) is

The springs shown in the figure are identical,each having a spring constant $K$. When mass $A = 4\, kg$ is attached,the elongation of the spring is $1\, cm$. If mass $B = 6\, kg$ is attached to the system of two springs in series as shown,the total elongation produced is ..... $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module