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The displacement of a particle executing simple harmonic motion is given by $y = A_0 + A \sin \omega t + B \cos \omega t$. Then the amplitude of its oscillation is given by:
In the nuclear emission stated above: ${}_{82}^{290}X \xrightarrow{\alpha} Y \xrightarrow{e^+} Z \xrightarrow{\beta^-} P \xrightarrow{e^-} Q$, the mass number and atomic number of the product Q respectively, are:
A second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket:
Two planets orbit a star in circular paths with radii $R$ and $4R$, respectively. At a specific time, the two planets and the star are aligned in a straight line. If the orbital period of the planet closest to the star is $T$, what is the minimum time after which the star and the planets will again be aligned in a straight line (at the initial position)?
A rocket is fired vertically upward with a speed of $v = \frac{v_e}{\sqrt{2}}$ from the Earth's surface, where $v_e$ is escape velocity on the surface of Earth. The distance from the surface of Earth upto which the rocket can go before returning to the Earth is: (given, the radius of Earth $R = 6400$ km)
A particle executes simple harmonic oscillation with an amplitude $A$. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:
Out of the following functions, which represents SHM? I. $y = \sin \omega t - \cos \omega t$ II. $y = \sin^3 \omega t$ III. $y = 5 \cos\left(\frac{3\pi}{4} - 3\omega t\right)$ IV. $y = 1 + \omega t + \omega^2 t^2$
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 $3\text{ s}$. When the mass $m$ is increased by $1\text{ kg}$, the time period of oscillations becomes $5\text{ s}$. The value of $m$ in kg is:
The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:
The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:
A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20 \text{ m/s}^2$ at a distance of $5 \text{ m}$ from the mean position. The time period of oscillation is:
During simple harmonic motion of a body, the energy at the extreme position is:
A radioactive nucleus ${}_Z^A X$ undergoes spontaneous decay in the sequence ${}_Z^A X \to {}_{Z-1} B \to {}_{Z-3} C \to {}_{Z-2} D$, where $Z$ is the atomic number of element $X$. The possible decay particles in the sequence are
The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended, the period of oscillation will now be:
The refracting angle of a prism is $A$, and refractive index of the material of the prism is $\cot(A/2)$. The angle of minimum deviation is:
A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^\circ$, the box starts to slip and slides $4.0 \text{ m}$ down the plank in $4.0 \text{ s}$. The coefficients of static and kinetic friction between the box and the plank will be, respectively:
The restoring force of a spring, with a block attached to the free end of the spring, is represented by:
The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^\circ$. One of the two refracting surfaces of the prism is made a mirror inwards with a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if the angle of incidence on the prism is:
Two pendulums of length $121 \text{ cm}$ and $100 \text{ cm}$ start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:
If the critical angle for total internal reflection from a medium to vacuum is $45^{\circ}$, the velocity of light in the medium is: