A block of mass 0.1 kg is connected to an elastic spring constant 640 and oscillates in a damping medium of damping constant . The system dissipates its energy gradually. The time taken for its mechanical energy of vibrations to drop to half of its initial value is closest to:
1. 2s
2. 3.5 s
3. 5 s
4. 7 s
In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii and . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be , the difference in radii, is best given by-
1. 1 cm
2. 0.1 cm
3. 0.5 cm
4. 0.01 cm
A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of . What is the force constant of the bonds connecting one atom with the orther? Molecular weight of silver=108 and Avogadro's number=.
1. 5.5 N/m
2. 6.4 N/m
3. 7.1 N/m
4. 2.2 N/m
A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along the x-direction about its equilibrium position, taken to be at x=0, with an amplitude A. An electric field E is applied along the x-direction. Which of the following statements is correct?
1. The new equilibrium position is at distance from x=0.
2. The total energy of the system is .
3. The total energy of the system is .
4. The new equilibrium position is at a distance from x=0.
Two simple harmonic motions as shown below, are at right angles. They are combined to form Lissajous figures.
x(t)=A sin (at+)
y(t)=B sin (bt)
Identify the correct match below:
Parameters Curve
1. Parabola
2. Line
3. Ellipse
4. Circle
A particle executes simple harmonic motion and is located at x=a, b and c at times respectively. The frequency of the oscillation is :
1.
2.
3.
4.
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half of its value for every 10 oscillations. The time it will take to drop to of the original amplitude is close to:
1. 100 s
2. 20 s
3. 10 s
4. 50 s
A simple pendulum oscillating in air has time period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:
1,
2.
3.
4.
A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in second is :
1.
2.
3.
4.
The displacement of a damped harmonic oscillator is given by
. Here t is in seconds. The time taken for its amplitude of vibrations to drop to half of its initial value is close to:
1. 13 s
2. 7 s
3. 27 s
4. 4 s
The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2s. The period of oscillation of the same pendulum on the planet would be:
1.
2.
3.
4.
A particle undergoing simple harmonic motion has time dependent displacement given by . The ratio of kinetic to potential energy of this particle at t=210 s will be:
1. 2
2.
3. 3
4. 1
A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations. If two masses each of mass 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to:
1. 0.17
2. 0.37
3. 0.57
4. 0.77
A body of mass M is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. when the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is.
1.
2.
3.
4.
The light identical spring of spring constant k is attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre 'O' and can rotate freely in the horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in the figure. The rod is gently pushed through a small angle and released. The frequency of the resulting oscillation is:
1.
2.
3.
4.