A particle executes a simple harmonic motion of time period $T$. Find the time taken by the particle to go directly from its mean position to half the amplitude
Medium
Download our app for free and get started
(d) $y = A\sin \omega t = \frac{{A\sin 2\pi }}{T}t$
==> $\frac{A}{2} = A\sin \frac{{2\pi t}}{T}$
==> $t = \frac{T}{{12}}$.
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 in $SHM $ is described by the displacement equation $x(t) = A\cos (\omega t + \theta ).$ If the initial $(t = 0)$ position of the particle is $1 \,cm$ and its initial velocity is $\pi $cm/s, what is its amplitude? The angular frequency of the particle is $\pi {s^{ - 1}}$
A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $\frac{2}{{\sqrt 5 }}$. After how many collisions the amplitude of vibration will become less than $60°$
Time period of a simple pendulum is $T$ inside a lift when the lift is stationary. If the lift moves upwards with an acceleration $g / 2,$ the time period of pendulum will be
A pendulume clock loses $12\;s$ a day if the temperature is $40^oC$ and gains $4\;s$ a day if the temperature is $20^oC$. The temperature at which the clock will show correct time, and the coeffecient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively
A rectangular block of mass $5\,kg$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1\,m$ and time period $3.14\,s$. The maximum force exerted by spring on block is $.......N$.
The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended, the period of oscillation will now be
A body oscillates with $S.H.M.$ according to the equation $x=(5.0 \,m ) \cos \left[\left(2 \pi \,rad s ^{-1}\right) t+\pi / 4\right]$ At $t=1.5 \,s$, its acceleration is ....... $m / s ^2$