The angular velocities of three bodies in simple harmonic motion are ${\omega _1},\,{\omega _2},\,{\omega _3}$ with their respective amplitudes as ${A_1},\,{A_2},\,{A_3}$. If all the three bodies have same mass and velocity, then
Easy
Download our app for free and get startedPlay store
(a)Velocity is same. So by using $v = a\omega $
==> ${A_1}{\omega _1} = {A_2}{\omega _2} = {A_3}{\omega _3}$
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    Initially system is in equilibrium. Time period of $SHM$ of block in vertical direction is
    View Solution
  • 2
    A metal rod of length ' $L$ ' and mass ' $m$ ' is pivoted at one end. A thin disk of mass ' $M$ ' and radius $'R'$ $( < L)$ is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case $A$) The disc is not free to rotate about its center and (case $B$) the disc is free to rotate about its center. The rod-disc system performs $SHM$ in vertical plane after being released from the same displaced position. Which of the following statement$(s)$ is (are) true? $Image$

    $(A)$ Restoring torque in case $A =$ Restoring torque in case $B$

    $(B)$ Restoring torque in case $A < $ Restoring torque in case $B$

    $(C)$ Angular frequency for case $A > $ Angular frequency for case $B$.

    $(D)$ Angular frequency for case $A < $ Angular frequency for case $B$.

    View Solution
  • 3
    A $1 \,kg$ block attached to a spring vibrates with a frequency of $1\, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8\, kg$ block placed on the same table. So, the frequency of vibration of the $8\, kg$ block is ..... $Hz$
    View Solution
  • 4
    Acceleration $A$ and time period $T$ of a body in $S.H.M.$ is given by a curve shown below. Then corresponding graph, between kinetic energy $(K.E.)$ and time $t$ is correctly represented by
    View Solution
  • 5
    A mass $m = 1.0\,kg$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is $500\,N/m.$ What is the amplitude $A$ of the motion, so that the mass $m$ tends to get detached from the pan ? (Take $g = 10\,m/s^2$ ). The spring is stiff enough so that it does not get distorted during the motion.
    View Solution
  • 6
    The motion of a simple pendulum excuting $S.H.M$. is represented by following equation.

    $Y = A \sin (\pi t +\phi)$, where time is measured in $second$.

    The length of pendulum is .............$cm$

    View Solution
  • 7
    A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2 ms ^{-1}$ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is $320 ms ^{-1}$, the smallest value of the percentage change required in the length of the pipe is. . . . . .
    View Solution
  • 8
    The periodic time of a simple pendulum of length $1\, m $ and amplitude $2 \,cm $ is $5\, seconds$. If the amplitude is made $4\, cm$, its periodic time in seconds will be
    View Solution
  • 9
    Time period of a simple pendulum is $T$ inside a lift when the lift is stationary. If the lift moves upwards with an acceleration $g / 2,$ the time period of pendulum will be
    View Solution
  • 10
    The maximum velocity of a particle, executing simple harmonic motion with an amplitude $7\ mm$, is $4.4\ m/s$. The period of oscillation is .... $sec$
    View Solution