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. ..... $kg/s$

  • A$9.8$
  • B$2.8$
  • C$98$
  • D$28$
Medium
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
    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
  • 2
    Select wrong statement about simple,harmonic motion
    View Solution
  • 3
    To make the frequency double of a spring oscillator, we have to
    View Solution
  • 4
    A block with mass $M$ is connected by a massless spring with stiffiess constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_0$. Consider two cases: ($i$) when the block is at $x_0$; and ($ii$) when the block is at $x=x_0+A$. In both the cases, a perticle with mass $m$ is placed on the mass $M$ ?

    ($A$) The amplitude of oscillation in the first case changes by a factor of $\sqrt{\frac{M}{m+M}}$, whereas in the second case it remains unchanged

    ($B$) The final time period of oscillation in both the cases is same

    ($C$) The total energy decreases in both the cases

    ($D$) The instantaneous speed at $x_0$ of the combined masses decreases in both the cases

    View Solution
  • 5
    The displacement of a particle executing $SHM$ is given by $y=0.25 \sin 200 t$ $cm$. The maximum speed of the particle is $.........cm s^{-1}$
    View Solution
  • 6
    Identify the correct statement 
    View Solution
  • 7
    If $A$ is the area of cross-section of a spring $L$ is its length $E$ is the Young's modulus of the material of the spring then time period and force constant of the spring will be respectively
    View Solution
  • 8
    The effective spring constant of two spring system as shown in figure will be 
    View Solution
  • 9
    The 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 be
    View Solution
  • 10
    If pendulum is released from given position find velocity of Bob when it reaches the lowest position
    View Solution