Astone is swinging in a horizontal circle $0.8\, m$ in diameter at $30 \,rev / min.$ Adistant horizontal light beam causes a shadow of the stone to be formed on a nearly vertical wall. The amplitude and period of the simple harmonic motion for the shadow of the stone are
Medium
Download our app for free and get startedPlay store
$A=\frac{d}{2}=\frac{0.8}{2}=0.4 \mathrm{m}$

$\omega=\frac{30 \times 2 \pi}{60}=\pi$

or $\frac{2 \pi}{\mathrm{T}}=\pi$

$\therefore \mathrm{T}=2 \mathrm{sec}$

art

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.*

Similar Questions

  • 1
    Two particles execute $SHM$ of same amplitude of $20\, cm$ with same period along the same line about the same equilibrium position. The maximum distance between the two is $20\, cm.$ Their phase difference in radians is
    View Solution
  • 2
    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 ..... $cm/s^2$
    View Solution
  • 3
    A spring mass system executes damped harmonic oscillations given by the equation 

    $y = A{e^{ - \frac{{bt}}{{2m}}}}\sin (\omega 't + \phi )$

    where the symbols have their usual meanings. If a $2\ kg$ mass $(m)$ is attached to a spring of force constant $(K)$ $1250\ N/m$ , the period of the oscillation is $\left( {\pi /12} \right)s$ . The damping constant $‘b’$ has the value. ..... $kg/s$

    View Solution
  • 4
    A particle performs $SHM$ on $x-$ axis with time period of $0.5\,sec,$ such that it's velocity is zero at $x = -3\,cm$ and at $x = 9\,cm$. It was located at $x = 0$ and moving in negative $'x'$ at $t = 0$. The equation of $SHM$ of the particle is
    View Solution
  • 5
    A particle moves in $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1-\cos \omega t)$ where $a$ and $\omega$ are constants. The particle traces
    View Solution
  • 6
    The length of a seconds pendulum is .... $cm$
    View Solution
  • 7
    Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is $100 g$. The time period of the motion of the particle will be (approximately) (take $g =10\,ms ^{-2}$, radius of earth $=6400\,km$ )
    View Solution
  • 8
    A simple pendulum is set into vibrations. The bob of the pendulum comes to rest after some time due to
    View Solution
  • 9
    The $x$-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=4 / 3 \mathrm{~s}$ is
    View Solution
  • 10
    The displacement $x$ (in metres) of a particle performing simple harmonic motion is related to time $t$ (in seconds) as $x = 0.05\cos \left( {4\,\pi \,t + \frac{\pi }{4}} \right)$. The frequency of the motion will be ..... $Hz$
    View Solution