The displacement of an oscillating particle varies with time (in seconds) according to the equation $y (cm) = sin \frac{\pi }{2}\left( {\frac{t}{2} + \frac{1}{3}} \right)$. The maximum acceleration of the particle is approximately ..... $cm/s^2$
A$5.21$
B$3.62$
C$1.81$
D$0.62$
Easy
Download our app for free and get started
D$0.62$
d ${a_{\max }} = {\omega ^2}a = {\left( {\frac{\pi }{4}} \right)^2}a = 0.62\;cm/se{c^2}$ $[ a =1]$
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.*
A particle of mass m is executing oscillations about the origin on the $X-$axis. Its potential energy is $U(x) = k{[x]^3}$, where $k$ is a positive constant. If the amplitude of oscillation is $a$, then its time period $T$ is
For a particle executing $S.H.M.,\, x =$ displacement from equilibrium position, $v =$ velocity at any instant and $a =$ acceleration at any instant, then
The amplitude and the periodic time of a $S.H.M.$ are $ 5\,cm$ and $6\,sec$ respectively. At a distance of $2.5\,cm$ away from the mean position, the phase will be
A mass $m$ attached to free end of a spring executes SHM with a period of $1\; s$. If the mass is increased by $3\; kg$ the period of oscillation increases by one second, the value of mass $m$ is $..............kg$.
Starting from the origin a body oscillates simple harmonically with a period of $2\ s$. After what time will its kinetic energy be $75\%$ of the total energy?
The period of small oscillation of a simple pendulum is $T$. The ratio of density of liquid to the density of material of the bob is $\rho \left( {\rho < 1} \right)$.When immersed in the liquid, the time period of small oscillation will now be
A spring has a certain mass suspended from it and its period for vertical oscillation is $T$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now
Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.06 m. Each spring has a natural length of 0.06$\pi$ m and force constant 0.1N/m. Initially both the balls are displaced by an angle $\theta = \pi /6$ radian with respect to the diameter $PQ$ of the circle and released from rest. The frequency of oscillation of the ball B is