A particle executes $SHM$ of period $1.2\, sec$ and amplitude $8\, cm.$ Find the time it takes to travel $3\,cm$ from the positive extremity of its oscillation.  ..... $\sec$
Medium
Download our app for free and get startedPlay store
$x=A \cos \omega t$

$\Rightarrow \quad 5 \mathrm{cm}=8 \cos \omega t$

$\Rightarrow \quad \omega t=0.9$

$\frac{2 \pi}{1.2} t=0.9$

$\Rightarrow \quad t=\frac{1.08}{2 \pi} \mathrm{s}=0.17 \mathrm{s}$

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
    Column $I$ gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column $II$. Match the set of parameters given in Column $I$ with the graph given in Column $II$. Indicate your answer by darkening the appropriate bubbles of the $4 \times 4$ matrix given in the $ORS$.
    Column $I$ Column $II$
    $(A)$ Potential energy of a simple pendulum (y axis) as a function of displacement ( $\mathrm{x}$ axis) $Image$
    $(B)$ Displacement (y axis) as a function of time (x axis) for a one dimensional motion at zero or constant acceleration when the body is moving along the positive $\mathrm{x}$-direction $Image$
    $(C)$ Range of a projectile (y axis) as a function of its velocity ( $\mathrm{x}$ axis) when projected at a fixed angle $Image$
    $(D)$ The square of the time period (y axis) of a simple pendulum as a function of its length ( $\mathrm{x}$ axis) $Image$

    View Solution
  • 2
    A block of mass $200\, g$ executing $SHM$ under the influence of a spring of spring constant $K=90\, N\,m^{-1}$ and a damping constant $b=40\, g\,s^{-1}$. The time elapsed for its amplitude to drop to half of its initial value is ...... $s$ (Given $ln\,\frac{1}{2} = -0.693$)
    View Solution
  • 3
    A particle executes simple harmonic motion. Its amplitude is $8 \,cm$ and time period is $6 \,s$. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ............. $s$
    View Solution
  • 4
    On a frictionless horizontal plane, a bob of mass $m=0.1 kg$ is attached to a spring with natural length $l_0=0.1 m$. The spring constant is $k_1=0.009 Nm ^{-1}$ when the length of the spring $I > l_0$ and is $k_2=0.016 Nm ^{-1}$ when $ I < l_0$. Initially the bob is released from $l=0.15 m$. Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is $T=(n \pi) s$, then the integer closest to $n$ is. . . . .
    View Solution
  • 5
    A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $(\theta)$ of thread deflection in the extreme position will be :
    View Solution
  • 6
    A particle performs $S.H.M.$ of amplitude $A$ with angular frequency $\omega$  along a straight line. Whenit is at a distance  $\frac{{\sqrt 3 }}{2}$ $A$  from mean position, its kinetic energy gets increased by an amount $\frac{1}{2}m{\omega ^2}{A^2}$  due to an impulsive force. Then its new amplitude becomes
    View Solution
  • 7
    The potential energy of a particle with displacement $X$ is $U(X)$. The motion is simple harmonic, when ($K$ is a positive constant)
    View Solution
  • 8
    The potential energy of a simple harmonic oscillator at mean position is $2\,joules$. If its mean $K.E.$ is $4\,joules$, its total energy will be .... $J$
    View Solution
  • 9
    The frequency of oscillations of a mass $m$ connected horizontally by a spring of spring constant $k$ is $4 Hz$. When the spring is replaced by two identical spring as shown in figure. Then the effective frequency is,
    View Solution
  • 10
    A pendulum bob has a speed of $3\, m/s$ at its lowest position. The pendulum is $0.5\, m$ long. The speed of the bob, when the length makes an angle of ${60^o}$ to the vertical, will be ..... $m/s$ (If $g = 10\,m/{s^2}$)
    View Solution