Two particles are executing S.H.M. The equation of their motion are ${y_1} = 10\sin \left( {\omega \,t + \frac{{\pi T}}{4}} \right),$ ${y_2} = 25\sin \,\left( {\omega \,t + \frac{{\sqrt 3 \pi T}}{4}} \right)$. What is the ratio of their amplitude
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A particle performs $S.H.M.$ of amplitude $A$ with angular frequency $\omega$ along a straight line. Whenit is at a distance $\frac{{\sqrt 3 }}{2}$ $A$ from mean position, its kinetic energy gets increased by an amount $\frac{1}{2}m{\omega ^2}{A^2}$ due to an impulsive force. Then its new amplitude becomes
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega $. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
A particle of mass m is under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F = - kx + {F_0}$ in which $k$ and ${F_0}$ are constants. The particle when disturbed will oscillate
A particle executes simple harmonic motion with an amplitude of $4 \mathrm{~cm}$. At the mean position, velocity of the particle is $10 \mathrm{~cm} / \mathrm{s}$. The distance of the particle from the mean position when its speed becomes $5 \mathrm{~cm} / \mathrm{s}$ is $\sqrt{\alpha} \mathrm{cm}$, where $\alpha=$____________.
The graphs in figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graphs best represents the relationship obtained when $y$ is The total energy of the system
A particle executing a simple harmonic motion of period $2\ s$ . When it is at its extreme displacement from its mean position, it receives an additional energy equal to what it had in its mean position. Due to this , in its subsequent motion,
A lift is descending with acceleration $g/3$ . What will be the time period of a simple pendulum suspended from its ceiling if its time period in staionary life is $'T'$ ?
The variation of kinetic energy $(KE)$ of a particle executing simple harmonic motion with the displacement $(x)$ starting from mean position to extreme position $(A)$ is given by