(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

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(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 $\frac{A_2}{A_1} = \sqrt{\frac{K_1}{K_2}}$.

Class 11 Physics Oscillations SHM of Spring Mass System

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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

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A
$\frac{K_1}{K_2}$
B
$\frac{K_2}{K_1}$
C
$\sqrt{\frac{K_1}{K_2}}$
D
$\sqrt{\frac{K_2}{K_1}}$

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$A$ block is fastened to a horizontal spring. The block is pulled to a distance $x = 10 \text{ cm}$ from its equilibrium position (at $x = 0$) on a frictionless surface from rest. The kinetic energy of the block at $x = 5 \text{ cm}$ is $0.25 \text{ J}$. The spring constant of the spring is nearly (in $\text{Nm}^{-1}$)

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$A$ 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:

MediumAIPMT 2002

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All the springs in figures $(a)$, $(b)$, and $(c)$ are identical, each having a force constant $K$. $A$ mass $m$ is attached to each system. If $T_a, T_b$, and $T_c$ are the periodic times of oscillation of the three systems in figures $(a)$, $(b)$, and $(c)$ respectively, then:

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$A$ mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period $T$. If the mass is increased by $m$,then the time period becomes $\frac{5}{4}T$. The ratio of $\frac{m}{M}$ is

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$A$ spring of length $l$ and force constant $k$ is attached to a mass $m$ and oscillates with frequency $f_1$. If the spring is cut into two equal parts and one part is attached to the same mass $m$ to oscillate,its frequency becomes $f_2$. Find the relation between $f_1$ and $f_2$.

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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

$A$ 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:

All the springs in figures $(a)$, $(b)$, and $(c)$ are identical, each having a force constant $K$. $A$ mass $m$ is attached to each system. If $T_a, T_b$, and $T_c$ are the periodic times of oscillation of the three systems in figures $(a)$, $(b)$, and $(c)$ respectively, then:

$A$ mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period $T$. If the mass is increased by $m$,then the time period becomes $\frac{5}{4}T$. The ratio of $\frac{m}{M}$ is

$A$ spring of length $l$ and force constant $k$ is attached to a mass $m$ and oscillates with frequency $f_1$. If the spring is cut into two equal parts and one part is attached to the same mass $m$ to oscillate,its frequency becomes $f_2$. Find the relation between $f_1$ and $f_2$.

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