The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5\ s$. In another $10\ s$ it will decrease to $\alpha $ times its original magnitude, where  $\alpha $ equals
  • A$0.6$
  • B$0.7$
  • C$0.81$
  • D$0.73$
JEE MAIN 2013, 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 small mass executes linear $SHM$ about $O$ with amplitude $a$ and period $T.$ Its displacement from $O$ at time $T/8$ after passing through $O$ is :
    View Solution
  • 2
    When the displacement is half the amplitude, the ratio of potential energy to the total energy is
    View Solution
  • 3
    For a simple pendulum, a graph is plotted between its kinetic energy $(KE)$ and potential energy $(PE)$ against its displacement $d$. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)
    View Solution
  • 4
    A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma $ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period $T$ of the oscillations of the cylinder will be
    View Solution
  • 5
    A spring has a certain mass suspended from it and its period for vertical oscillation is $T$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now
    View Solution
  • 6
    If a Second's pendulum is moved to a planet where acceleration due to gravity is $4$ times, the length of the second's pendulum on the planet should be made .......... times
    View Solution
  • 7
    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 $60°$
    View Solution
  • 8
    A mass $m$ is attached to two springs of same force constant $K$, as shown in following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillation in the following arrangements, in which case time period is maximum?
    View Solution
  • 9
    As per given figures, two springs of spring constants $K$ and $2\,K$ are connected to mass $m$. If the period of oscillation in figure $(a)$ is $3 s$, then the period of oscillation in figure $(b)$ will be $\sqrt{ x }$ s. The value of $x$ is$.........$
    View Solution
  • 10
    A $5\, kg$ collar is attached to a spring of spring constant $500\, Nm^{-1}$. It slides without friction over a horizontal rod. The collar is displaced from its equillibrium position by $10\, cm$ and released. The time period of oscillation is
    View Solution