What is the maximum acceleration of the particle doing the $SHM$ $y = 2\sin \left[ {\frac{{\pi t}}{2} + \phi } \right]$ where $2$ is in $cm$
Easy
Download our app for free and get started
(b) Comparing given equation with standard equation,
$y = a\sin (\omega t + \phi ),$ we get, $a = 2\,cm,$ $\omega = \frac{\pi }{2}$
$\therefore {A_{max}} = {\omega ^2}A$ $= {\left( {\frac{\pi }{2}} \right)^2} \times 2$ $ = \frac{{{\pi ^2}}}{2}\,cm/{s^2}$.
$y = a\sin (\omega t + \phi ),$ we get, $a = 2\,cm,$ $\omega = \frac{\pi }{2}$
$\therefore {A_{max}} = {\omega ^2}A$ $= {\left( {\frac{\pi }{2}} \right)^2} \times 2$ $ = \frac{{{\pi ^2}}}{2}\,cm/{s^2}$.
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
- 1A particle executes $SHM$ with amplitude of $20 \,cm$ and time period is $12\, sec$. What is the minimum time required for it to move between two points $10\, cm$ on either side of the mean position ..... $\sec$ ?View Solution
- 2A particle executing $S.H.M.$ its potential energy $V/S$ displacement graph is given by The value of restoring force constant is ..... $N/m$View Solution
- 3A particle executes simple harmonic motion along a straight line with an amplitude $A$. The potential energy is maximum when the displacement isView Solution
- 4The resultant of two rectangular simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by $\frac{\pi }{2}$ isView Solution
- 5View SolutionThe graph between velocity and position for a damped oscillation will be
- 6particle moves with simple harmonic motion in a straight line. In first $\tau\ s$, after starting from rest it travels a distance $a$, and in next $\tau\ s$ it travels $2a$, in same direction, thenView Solution
- 7View SolutionIn case of damped oscillation frequency of oscillation is ............
- 8The amplitude and the time period in a $S.H.M.$ is $0.5 \,cm$ and $0.4 \,sec$ respectively. If the initial phase is $\pi /2$ radian, then the equation of $S.H.M.$ will beView Solution
- 9View SolutionA system exhibiting S.H.M. must possess
- 10A particle executes simple harmonic motion with a frequency $f$. The frequency with which its kinetic energy oscillates isView Solution