Two bodies $M$ and $N $ of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude $M$ to that of $N$ is
A$\frac{{{k_1}}}{{{k_2}}}$
B$\sqrt {\frac{{{k_1}}}{{{k_2}}}} $
C$\frac{{{k_2}}}{{{k_1}}}$
D$\sqrt {\frac{{{k_2}}}{{{k_1}}}} $
AIEEE 2003,IIT 1988, Medium
Download our app for free and get started
D$\sqrt {\frac{{{k_2}}}{{{k_1}}}} $
d (d) Maximum velocity $ = a\omega = a\sqrt {\frac{k}{m}} $
Given that ${a_1}\sqrt {\frac{{{K_1}}}{m}} = {a_2}\sqrt {\frac{{{K_2}}}{m}} $
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.*
Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ is
A simple pendulum has time period $T_1$. The point of suspension is now moved upward according to equation $y = k{t^2}$ where $k = 1\,m/se{c^2}$. If new time period is $T_2$ then ratio $\frac{{T_1^2}}{{T_2^2}}$ will be
Three simple harmonic motions of equal amplitudes $A$ and equal time periods in the same direction combine. The phase of the second motion is $60^o$ ahead of the first and the phase of the third motion is $60^o$ ahead of the second. Find the amplitude of the resultant motion
For any $S.H.M.$, amplitude is $6\, cm$. If instantaneous potential energy is half the total energy then distance of particle from its mean position is .... $cm$
A particle is executing $SHM$ of amplitude $A,$ about the mean position $x = 0.$ Which of the following cannot be a possible phase difference between the positions of the particle at $x = +\,A/2$ and $x = - A/\sqrt {2} .$
A cylindrical piston of mass $M$ slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be
The maximum speed of a particle executing $S.H.M.$ is $1\,m/s$ and its maximum acceleration is $1.57\,m/se{c^2}$. The time period of the particle will be .... $\sec$
Springs of spring constants $K, 2K, 4K, 8K,$ ..... are connected in series. A mass $40\, gm$ is attached to the lower end of last spring and the system is allowed to vibrate. What is the time period of oscillation ..... $\sec$. (Given $K = 2\, N/cm$)
Abody performs simple harmonic oscillations along the straight line $ABCDE$ with $C$ as the midpoint of $AE.$ Its kinetic energies at $B$ and $D$ are each one fourth of its maximum value. If $AE = 2R,$ the distance between $B$ and $D$ is