A load of mass $m$ falls from a height $h$ on to the scale pan hung from the spring as shown in the figure. If the spring constant is $k$ and mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is
  • A$mg / d$
  • B$\frac{ mg }{ k } \sqrt{\left(\frac{1+2 hk }{ mg }\right)}$
  • C$\frac{ mg }{ k }+\frac{ mg }{ k } \sqrt{\left(\frac{1+2 hk }{ mg }\right)}$
  • D$\frac{ mg }{ k } \sqrt{\left(\frac{1+2 hk }{ mg }-\frac{ mg }{ k }\right)}$
Diffcult
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
    The amplitude of a particle executing $S.H.M.$ with frequency of $60 \,Hz$ is $0.01 \,m$. The maximum value of the acceleration of the particle is
    View Solution
  • 2
    A mass of $0.2\,kg$ is attached to the lower end of a massless spring of force-constant $200\, N/m,$ the upper end of which is fixed to a rigid support. Which of the following statements is/are true ?
    View Solution
  • 3
    The total energy of a particle executing S.H.M. is proportional to
    View Solution
  • 4
    Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is $x(t)$ vs. $p(t)$ curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative. $Image$

    $1.$ The phase space diagram for a ball thrown vertically up from ground is

    mcq $Image$

    $2.$ The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_1$ and $E_2$ are the total mechanical energies respectively. Then $Image$

    $(A)$ $ E_1=\sqrt{2} E_2$ $(B)$ $ E_1=2 E_2$

    $(C)$ $ E_1=4 E_2$ $(D)$ $ E_1=16 E_2$

    $3.$ Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is $Image$

    mcq $Image$

    Give the answer question $1,2$ and $3.$

    View Solution
  • 5
    Which of the following equation does not represent a simple harmonic motion
    View Solution
  • 6
    A particle of mass m is executing oscillations about the origin on the $X-$axis. Its potential energy is $U(x) = k{[x]^3}$, where $k$ is a positive constant. If the amplitude of oscillation is $a$, then its time period $T$ is
    View Solution
  • 7
    The length of a simple pendulum is increased by $2\%$. Its time period will
    View Solution
  • 8
    A pendulum suspended from the ceiling of a train has a period $T$, when the train is at rest. When the train is accelerating with a uniform acceleration a, the period of oscillation will
    View Solution
  • 9
    This is the position time graph of a mass on spring. What can you say about the velocity and force at the instant indicated by dashed line ? (positive direction is to the right)
    View Solution
  • 10
    A simple harmonic oscillator has an amplitude a and time period $T$. The time required by it to travel from $x = a$ to $x = \frac{a }{2}$ is
    View Solution