A particle executes linear simple harmonic motion with an amplitude of $2\, cm$. When the particle is at $1\, cm$ from the mean position the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
Medium
Download our app for free and get started
(c) Velocity $v = \omega \sqrt {{A^2} - {x^2}} $ and acceleration $ = {\omega ^2}x$
Now given, ${\omega ^2}x = \omega \sqrt {{A^2} - {x^2}} $
==> ${\omega ^2}.1 = \omega \sqrt {{2^2} - {1^2}} $
==> $\omega = \sqrt 3 $
$T = \frac{{2\pi }}{\omega } = \frac{{2\pi }}{{\sqrt 3 }}$
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
- 1Two springs of constant ${k_1}$and ${k_2}$are joined in series. The effective spring constant of the combination is given byView Solution
- 2The length of a seconds pendulum is .... $cm$View Solution
- 3View SolutionWhich of the following is a necessary and sufficient condition for S.H.M.
- 4View SolutionAn assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. Initially the springs are relaxed. The left mass is displaced to the left while the right mass is displaced to the right and released. The resulting collision is elastic. The time period of the oscillations of the system is :-
- 5Two simple harmonic motions of angular frequency $100$ and $1000\,\,rad\,s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration isView Solution
- 6Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $K$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system. The amplitude of oscillations isView Solution
- 7Figure shows the position-time graph of an object in $S.H.M.$ The correct equation representing this motion is ..........View Solution
- 8A $1 \,kg$ block attached to a spring vibrates with a frequency of $1\, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8\, kg$ block placed on the same table. So, the frequency of vibration of the $8\, kg$ block is ..... $Hz$View Solution
- 9The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ isView Solution
- 10The amplitude of a particle executing $SHM$ is $4 \,cm$. At the mean position the speed of the particle is $16\, cm/sec$. The distance of the particle from the mean position at which the speed of the particle becomes $8\sqrt 3 \,cm/s,$ will be .... $cm$View Solution