Oscillations

Which of the following does not affect the period of a mass-spring system?

The motion of a particle is given by $x = 3 \sin(2\pi t + \pi/4)$. What is the time period of the motion?

If the amplitude of a simple harmonic oscillator is doubled, its total energy becomes:

The graph of potential energy vs displacement for a particle in SHM is a:

A block of mass $m$ is placed on top of a larger block of mass $M$, which is connected to a horizontal spring of spring constant $k$. The system rests on a frictionless horizontal surface. The coefficient of static friction between the two blocks is $\mu$. What is the maximum amplitude of oscillation that the system can have without the upper block slipping relative to the lower block?

A second's pendulum has a period of $2$ seconds. If its length is increased by $100\%$, the new period will be:

The phase of a particle in SHM at $t=0$ is called:

Two simple pendulums of length $100$ cm and $121$ cm start swinging together. After how many oscillations of the smaller pendulum will they again be in phase?

A block of mass $m$ is connected to a spring of constant $k$ and is placed on a smooth horizontal surface. The other end of the spring is fixed to a wall. If the block is pushed by a force $F$ and released, the amplitude of oscillation is:

The displacement of a particle executing SHM is $x = A \sin \omega t$. The ratio of the average velocity over half a cycle (from $x=0$ to $x=0$ via $A$) to the maximum velocity is:

When the displacement of a particle in SHM is half of its amplitude ($x = A/2$), the magnitude of its acceleration is:

A particle performs SHM with frequency $f$. The frequency with which its velocity changes direction is:

If the acceleration of a particle in SHM is $a$ and its displacement is $x$, which of the following is constant?

In the relation $a = - \omega^2 x$, what does the negative sign signify?

A particle is executing SHM with displacement $x = A \sin(\omega t)$. What is its velocity at $t = T/4$?

If the maximum acceleration of a particle is $a_m$ and the maximum velocity is $v_m$, which of the following expressions gives the amplitude $A$ of the oscillation?

A mass of $2\, \text{kg}$ undergoes SHM with a maximum velocity of $10\, \text{m/s}$. What is the maximum kinetic energy of the system?

If $x = A\sin(\omega t)$ and $y = A\sin(2\omega t)$, then for a particle moving in the $xy$-plane, the acceleration vector at $t=0$ is:

In SHM, the magnitude of the displacement is $x$ and the magnitude of acceleration is $a$. The graph between $a$ and $x$ is a straight line through the origin. What does the area under the $a$ vs $x$ graph from $0$ to $A$ represent?

A particle is moving in SHM. The ratio of its acceleration to its displacement is $k$ at $t=t_1$ and $4k$ at $t=t_2$. This statement is:

In SHM, the potential energy is zero at $t = 0$. What is the phase constant $\phi$ if $x = A \sin(\omega t + \phi)$?

The expression for total energy in terms of mass $m$, period $T$ and amplitude $A$ is:

If the total energy of a particle in SHM is $E$, its potential energy at $x = A$ is:

The sum of kinetic and potential energy of a particle in SHM is $E$. At distance $x$ from the mean position, the sum is:

The potential energy of a simple harmonic oscillator at displacement $x$ is $U$. What is its potential energy at displacement $2x$ (assuming $2x < A$)?

A particle of mass $m$ is executing SHM with amplitude $A$. The slope of the graph of kinetic energy $K$ against $x^2$ is:

If the period of SHM is $T$, at what time $t$ (starting from mean) is the potential energy of the particle 75% of the total energy?

A particle is moving such that its kinetic energy $K$ depends on displacement $x$ as $K = K_0 - \beta x^2$. The frequency of its motion is:

A body of mass $m$ is executing SHM with amplitude $A$. When its displacement is $x$, its kinetic energy is $K$ and potential energy is $U$. The value of $x$ for which $K=U$ is:

The average kinetic energy of a harmonic oscillator is $2$ J. Its maximum potential energy is:

What is the total distance traveled by the bob of a simple pendulum in one full oscillation if the amplitude is 'A'?

The restoring torque on a simple pendulum of length $l$ and mass $m$ for a small displacement $\theta$ is:

The angular frequency ($\omega$) of a simple pendulum is given by:

The time period of a simple pendulum is $2$ s. What is the length of the pendulum if $g = \pi^2$ m/s$^2$?

When the displacement of a simple pendulum is half its amplitude, the ratio of its kinetic energy to its potential energy is:

The displacement of a simple pendulum is given by $x = A \cos(\omega t + \phi)$. If at $t = 0$, the bob is at the mean position and moving towards the positive extreme, the phase constant $\phi$ is:

If a simple pendulum of length $l$ is placed on an inclined plane making an angle $\alpha$ with the horizontal, and the plane is frictionless, the time period of oscillation in the plane is:

A simple pendulum of length $L$ oscillates such that the string is horizontal at the extremes. What is the acceleration of the bob at the extreme position?

Which of the following does NOT affect the period of a simple pendulum (for small angles)?

For a simple pendulum, the ratio of the maximum kinetic energy to the maximum potential energy (measured from the lowest point) is:

Which property of a periodic motion stays constant in an ideal case?

Which of the following is the time period of the hour hand of a clock?

The motion of the hands of a clock is:

If the period of a vibration is $0.002$ seconds, the frequency is:

If $T$ is the period of SHM, then the period of its potential energy is:

The restoring force in a SHM is $F = -kx$. The potential energy $U$ is zero at $x=0$. What is the value of $U$ at $x$?

The length of a simple pendulum is $l$. If the pendulum is in a lift moving upwards with an acceleration $a$, its new time period will be:

In forced oscillations, if the frequency of the driving force is much greater than the natural frequency, the phase difference between the displacement and the driving force is approximately:

Which of the following represents a SHM?

A test tube of mass $m$ and cross-section $A$ is floating in a liquid of density $\rho$. It contains some lead shots such that the total mass is $M$. If it is slightly depressed and released, the period of SHM is:

The maximum acceleration of a particle in SHM is:

The relation between frequency ($f$) and time period ($T$) is:

The work done by the restoring force in one complete cycle of SHM is:

The time period of a simple pendulum is independent of:

A particle moves in a counter-clockwise direction on a reference circle of radius $R$. At $t = 0$, its projection on the $x$-axis is $x = -R/2$ and the particle is moving away from the equilibrium position (origin). If the displacement of the projection at any time $t$ is represented by the equation $x(t) = R \cos(\omega t + \phi)$, what is the value of the initial phase $\phi$?

At the mean position of a particle in SHM:

A particle in SHM has acceleration $a = -16x$ (in SI units). The angular frequency $\omega$ is:

A uniform rod of length $L$ is pivoted at one end and allowed to oscillate in a vertical plane. The time period of small oscillations is:

When a mass $m$ is connected to a spring of constant $k$, the frequency is $f_1$. When the mass is connected to another spring of constant $k_2$, the frequency is $f_2$. If the same mass is connected to the two springs in parallel, the new frequency $f$ will be:

A particle moves such that its acceleration $a$ is given by $a = -bx$, where $x$ is the displacement from the equilibrium position and $b$ is a positive constant. The period of oscillation is:

A restoring force of $4\ N$ acts on a particle at a displacement of $2\ cm$. The force constant is:

If the force constant $k$ is doubled and the displacement $x$ is halved, the restoring force:

In $F = -kx$, if $x$ is measured in cm and $F$ in dynes, the unit of $k$ is:

The force constant $k$ is numerically equal to the force required to produce:

If $F = -kx$ is the restoring force, what is the potential energy stored in the system at displacement $x$?

The restoring force in SHM is a conservative force. This means that:

For a particle in SHM, if the mass is doubled and the force constant is halved, the new time period $T'$ in terms of the old time period $T$ is:

A liquid of density $\rho$ is in a U-tube. One arm is vertical and the other is inclined at an angle $\theta$ to the vertical. If the liquid column of length $L$ is displaced by $x$, the restoring force constant is:

A particle of mass $m$ is attached to a spring of constant $k$ and is rotating in a horizontal circle of radius $R$ with angular velocity $\Omega$. The spring's natural length is $L$. The effective force constant for radial oscillations is:

If the displacement of a particle in SHM is $x = A \cos(\omega t + \phi)$, the force acting on it at $t=0$ is: