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

$A$ mass $m$ attached to the free end of a spring executes $SHM$ with a period of $1\; s$. If the mass is increased by $3\; kg$,the period of oscillation increases by $1\; s$. The value of mass $m$ is $..............kg$.

$A$ system consisting of three masses attached to a spring is in equilibrium. When the $700\,g$ mass is removed,the system oscillates with a period of $3\,s$. When the $500\,g$ mass is also removed,what will be the new time period of the system? (in $\text{seconds}$)

If a body of mass $0.98\, kg$ is made to oscillate on a spring of force constant $4.84\, N/m$,the angular frequency of the body is ..... $rad/s$. (in $.22$)

$A$ body of mass $5\; kg$ hangs from a spring and oscillates with a time period of $2\pi\; s$. If the body is removed,the length of the spring will decrease by:

$A$ coin is placed on a horizontal platform. The platform performs vertical simple harmonic motion with an angular frequency $\omega$. The amplitude of oscillation is gradually increased. At what condition will the coin first lose contact with the platform?

Vedclass Test Series

Exam Paper Generator

Online Exam Module