Questions in Oscillations

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The kinetic energy of a particle executing S.H.M. is 16 J when it is at its mean position. If the mass of the particle is 0.32 kg, then what is the maximum velocity of the particle
Consider the following statements. The total energy of a particle executing simple harmonic motion depends on its (1) Amplitude (2) Period (3) Displacement. Of these statements
A particle starts simple harmonic motion from the mean position. Its amplitude is a and total energy $E$. At one instant its kinetic energy is $3E/4.$ Its displacement at that instant is
A particle executes simple harmonic motion with a frequency $f$. The frequency with which its kinetic energy oscillates is
The amplitude of a particle executing SHM is made three-fourth keeping its time period constant. Its total energy will be
A particle of mass m is hanging vertically by an ideal spring of force constant K. If the mass is made to oscillate vertically, its total energy is
A body is moving in a room with a velocity of 20 m / s perpendicular to the two walls separated by 5 meters. There is no friction and the collisions with the walls are elastic. The motion of the body is
A body is executing Simple Harmonic Motion. At a displacement $x$ its potential energy is ${{E}_{1}}$ and at a displacement y its potential energy is ${{E}_{2}}$. The potential energy $E$ at displacement $(x+y)$ is
A particle moves such that its acceleration $a$ is given by $a=-bx$, where $x$ is the displacement from equilibrium position and $b$ is a constant. The period of oscillation is
The equation of motion of a particle is $\frac{{{d}^{2}}y}{d{{t}^{2}}}+Ky=0$, where K is positive constant. The time period of the motion is given by

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