Simple Harmonic Motion - Physics PYQ (Mechanics)

A block of mass \(\mathrm{l} \mathrm{kg}\) is fastened to a spring of spring constant of \(100 ~\mathrm{Nm}^{-1}\). The block is pulled to a distance \(x=10 \mathrm{~cm}\) from its equilibrium position \((x=0 \mathrm{~cm})\) on a frictionless surface, from rest at \(t=0\). The kinetic energy and the potential energy of the block when it is \(5 \mathrm{~cm}\) away from the mean position is

The scale of a spring balance which can measure from 0 to \(15 \mathrm{~kg}\) is \(0.25 \mathrm{~m}\) long. If a body suspended from this balance oscillates with a time period \(\frac{2 \pi}{5} \mathrm{~s}\), neglecting the mass of the spring, find the mass of the body suspended.

A spring is stretched by 0.40 m when a mass of 0.6 kg is suspended from it. The period of oscillations of the spring loaded by 255 g and put to oscillations is close to (g = 10 ms\(^{-2}\))

A heavy brass sphere is hung from a spring and it executes vertical vibrations with period T. The sphere is now immersed in a non-viscous liquid with a density (1/10 )th that of brass. When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will be

In case of a forced vibration, the resonance wave becomes very sharp when the

A particle executing simple harmonic motion along a straight line with an amplitude A, attains maximum potential energy when its displacement from mean position equals

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out the time period of oscillation would

A body is executing S.H.M. At a displacement \(x\) its potential energy is 9 J and at a displacement \(y\) its potential energy is 16 J . The potential energy at displacement \((x+y)\) is

An object undergoing simple harmonic motion takes 0.5 s to travel from one point of zero velocity to the next such point. The angular frequency of the motion is

A hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density \(\rho\). If the mass of hydrometer is \(m\) and the radius of the hydrometer tube is \(r\), then the time period of oscillation is

A cone with half the density of water is floating in water as shown in figure. It is depressed down by a small distance \(\delta(\ll< H)\) and released. The frequency of simple harmonic oscillations of the cone is

If the amplitude of a lightly damped oscillator decreases by \(1.5 \%\) then the mechanical energy of the oscillator lost in each cycle is

A particle is executing simple harmonic motion with an instantaneous displacement \(x=A \sin ^2\left(\omega t-\frac{\pi}{4}\right)\). The time period of oscillation of the particle is