The displacement of a particle from its mean position (in metre) is given by
$y = 0.2\sin \left( {10\pi t + 1.5\pi } \right)\cos \left( {10\pi t + 1.5\pi } \right)$
The motion of particle is
Medium
Download our app for free and get started
$\mathrm{y}=0.2 \sin (10 \pi \mathrm{t}+1.5 \pi) \cos (10 \pi \mathrm{t}+1.5 \pi)$
$=0.1 \sin 2(10 \pi \mathrm{t}+1.5 \pi)$
$[\because \sin 2 A=2 \sin A \cos A]$
$=0.1 \sin (20 \pi t+3.0 \pi)$
Time period, $T=\frac{2 \pi}{\omega}=\frac{2 \pi}{20 \pi}=\frac{1}{10}=0.1 \mathrm{sec}$
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
- 1The length of a seconds pendulum at a height $h=2 R$ from earth surface will be.(Given: $R =$ Radius of earth and acceleration due to gravity at the surface of earth $g =\pi^{2}\,m / s ^{-2}$ )View Solution
- 2A 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 ..... $J$View Solution
- 3View SolutionThe velocity of simple pendulum is maximum at
- 4Spring of spring constant $1200\, Nm^{-1}$ is mounted on a smooth frictionless surface and attached to a block of mass $3\, kg$. Block is pulled $2\, cm$ to the right and released. The angular frequency of oscillation is .... $ rad/sec$View Solution
- 5Length of a simple pendulum is $l$ and its maximum angular displacement is $\theta$, then its maximum $K.E.$ isView Solution
- 6Two springs with spring constants ${K_1} = 1500\,N/m$ and ${K_2} = 3000\,N/m$ are stretched by the same force. The ratio of potential energy stored in spring will beView Solution
- 7For a particle showing motion under the force $F=-5(x-2)^2$, the motion is .......View Solution
- 8Two particles P and Q describe S.H.M. of same amplitude $a$, same frequency $f$ along the same straight line. The maximum distance between the two particles is a $\sqrt{2}$.The initial phase difference between the particle is -View Solution
- 9A plank with a small block on top of it is under going vertical $SHM.$ Its period is $2\, sec.$ The minimum amplitude at which the block will separate from plank is :View Solution
- 10Two particles executing $S.H.M.$ of same frequency, meet at $x=+A / 2$, while moving in opposite directions. Phase difference between the particles is .........View Solution