Simple Harmonic Motion · Physics · AP EAPCET

As shown in the figure, two blocks of masses $m_1$ and $m_2$ are connected to spring of force constant $k$. The blocks are slightly displaced in opposite directions to $x_1, x_2$ distances and released. If the system executes simple harmonic motion, then the frequency of oscillation of the system ( $\omega$ ) is

The displacement of a particle of mass 2 g executing simple harmonic motion is $x=8 \cos \left(50 t+\frac{\pi}{12}\right) \mathrm{m}$, where $t$ is time in second. The maximum kinetic energy of the particle is

Two simple harmonic motions are represented by $y_1=5[\sin 2 \pi t+\sqrt{3} \cos 2 \pi t]$ and $y_2=5 \sin \left[2 \pi t+\frac{\pi}{4}\right]$. The ratio of their amplitudes is

When a mass $m$ is connected individually to the springs $k_1$ and $k_2$, the oscillation frequencies are $v_1$ and $v_2$. If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be

One bar magnet is in simple harmonic motion with time period $T$ in an earth's magnetic field. If its mass is increased by 9 times the time period becomes

In a spring block system as shown in figure. If the spring constant $k=9 \pi^2 \mathrm{Nm}^{-1}$, then the time period of oscillation is

A 3 kg block is connected as shown in the figure. Spring constants of two springs $k_1$ and $k_2$ are $50 \mathrm{Nm}^{-1}$ and $150 \mathrm{Nm}^{-1}$ respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is $\left(g=10 \mathrm{~ms}^{-2}\right)$

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

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 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

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

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 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

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 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