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 ..... $J$
Easy
Download our app for free and get started
(b) So $a = 6cm,\;\omega = 100\,rad/\sec $
${K_{\max }} = \frac{1}{2}m{\omega ^2}{a^2}$
${K_{\max }} = \frac{1}{2}m{\omega ^2}{a^2}$
$= \frac{1}{2} \times 1 \times {(100)^2} \times {(6 \times {10^{ - 2}})^2} $
$= 18\;J$
Download our appand 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
- 1View SolutionSelect wrong statement about simple,harmonic motion
- 2Two $SHM$ are represented by equations, $y_1 = 6\cos \left( {6\pi t + \frac{\pi }{6}} \right)\,,{y_2} = 3\left( {\sqrt 3 \sin 3\pi t + \cos 3\pi t} \right)$View Solution
- 3A simple pendulum having length $\ell $ is having speed $\sqrt {2g\ell }$ at bottom most point of its trajectory. Its motion will beView Solution
- 4Two identical spring of constant $K$ are connected in series and parallel as shown in figure. A mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will beView Solution
- 5If a spring extends by $x$ on loading, then energy stored by the spring is (if $T$ is the tension in the spring and $K$ is the spring constant)View Solution
- 6View SolutionIn damped oscillation graph between velocity and position will be
- 7The velocity of a particle executing SHM varies with displacement $( x )$ as $4 v ^2=50- x ^2$. The time period of oscillations is $\frac{x}{7} s$. The value of $x$ is $............$ $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$View Solution
- 8The potential energy of a particle executing S.H.M. is $ 2.5\, J$, when its displacement is half of amplitude. The total energy of the particle be .... $J$View Solution
- 9A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K _1$ and $K _2$. For the frictionless surface, the time period of oscillation of mass $m$ isView Solution
- 10Three masses $700g, 500g$, and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3$ seconds, when the $500 \,gm$ mass is also removed, it will oscillate with a period of ...... $s$View Solution
