A body of mass $1\,kg$ is executing simple harmonic motion. Its displacement $y(cm)$ at $t$ seconds is given by $y = 6\sin (100t + \pi /4)$. Its maximum kinetic energy is ..... $J$
A$6$
B$18$
C$24$
D$36$
Easy
Download our app for free and get started
B$18$
b (b) So $a = 6cm,\;\omega = 100\,rad/\sec $
${K_{\max }} = \frac{1}{2}m{\omega ^2}{a^2}$
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.*
The displacement of a particle moving in $S.H.M.$ at any instant is given by $y = a\sin \omega t$. The acceleration after time $t = \frac{T}{4}$ is (where $T$ is the time period)
Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be
A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma $ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period $T$ of the oscillations of the cylinder will be
The amplitude of vibration of a particle is given by ${a_m} = ({a_0})/(a{\omega ^2} - b\omega + c);$ where ${a_0},a,b$ and $c$ are positive. The condition for a single resonant frequency is
A spring whose unstretched length is $\ell $ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $\ell_1$ and $\ell_2$ where, $\ell_1 = n\ell_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants, $k_1$ and $k_2$ will be
A pendulum has time period $T$. If it is taken on to another planet having acceleration due to gravity half and mass $ 9 $ times that of the earth then its time period on the other planet will be
A ring of diameter $2m$ oscillates as a compound pendulum about a horizontal axis passing through a point at its rim. It oscillates such that its centre move in a plane which is perpendicular to the plane of the ring. The equivalent length of the simple pendulum is .... $m$
Two blocks $A$ and $B$ each of mass m are connected by a massless spring of natural length L and spring constant $K$. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown in figure. A third identical block $C$ also of mass $m$ moves on the floor with a speed $v$ along the line joining $A$ and $B$ and collides with $A$. Then