#### When a particle moves along the circumference of a circle with uniform speed, the displacement of its projection along the X axis, varies ____.

When a particle moves along the circumference of a circle with uniform speed, the displacement of its projection along the X axis, varies sinusoidally.

#### For a linear harmonic oscillator, the force is: (i) always directed to the mean position (ii) directly proportional to the displacement.

For a linear harmonic oscillator, the force is always directed to the mean position and is directly proportional to the displacement.

#### If a particle executes uniform circular motion along a reference circle, then its projection along the X or Y axis executes ____.

If a particle executes uniform circular motion along a reference circle, and then its projection along the X or Y axis executes simple harmonic motion.

#### The total energy of a harmonic oscillator ____.

The total energy of a harmonic oscillator is independent of time.

#### The vibrations that are sustained under the action of an external periodic force are called ____oscillations.

The vibrations that are sustained under the action of an external periodic force are called forced oscillations.

#### A block of mass 2 kg is attached to a spring and executes simple harmonic motion. The spring constant of the spring is 50 N/m. Its potential energy when the displacement is 5 cm is ____ J.

Here, displacement of the block, x = 5 cm = 0.05 m

The force constant of the spring, k = 50 N/m

Potential energy of the block, PE=(1/2)kx^{2}

=1/2×50×(0.05)^{2}

= 62.5 × 10^{−3} J

#### For a particle executing simple harmonic motion, the phase difference between its acceleration and velocity is ____.

For a particle executing simple harmonic motion, the phase difference between its acceleration and velocity is π/2radian, which is equal to 90°.

#### When a linear harmonic oscillator is at its mean position: (i) its potential energy is maximum (ii) its kinetic energy is maximum (iii) its kinetic energy is equal to its total energy (iv)its potential energy is equal to its total energy.

When a linear harmonic oscillator is at its mean position, it has maximum velocity and hence, its kinetic energy is maximum, which is equal to its total energy.

#### When a loaded spring executes oscillations: (i) it is the restoring force that brings back the load to its mean position (ii) the magnitude of the restoring force is directly proportional to the displacement of the load (iii) the restoring force is always directed to the mean position

When a loaded spring executes oscillations it is the restoring force that brings back the load to its mean position. The magnitude of the restoring force is directly proportional to the displacement of the load and it is always directed to the mean position.

#### For a particle executing simple harmonic motion, the phase difference between its acceleration and displacement is ____.

For a particle executing simple harmonic motion, the phase difference between its acceleration and displacement is 180°, which is π radian.

#### An external force is necessary to keep a pendulum oscillating in the presence of damping forces.

An external force is necessary to keep a pendulum oscillating in the presence of damping forces.

#### A load of mass 2 kg is attached to a spring of constant 200 N/m. The system executes simple harmonic motion. The time period of oscillation is ____ s.

Given, mass of the load, m = 2 kg Spring constant, k = 20 N/m The time period, T=2π √m/k =2π √2/200 =2π/10=π/5 s

#### For a particle executing simple harmonic motion, the phase difference between its velocity and displacement is ___ radian.

For a particle executing simple harmonic motion, the phase difference between its velocity and displacement is π/2.

#### A periodic motion where the displacement of an oscillating particle varies sinusoidally with the time t can be called as simple harmonic motion.

A periodic motion where the displacement of an oscillating particle varies sinusoidally with the time t can be called as simple harmonic motion.

#### Select the odd choice among the given ones.

Bob of a pendulum executes oscillatory motion whereas the blades of a turbine, a wind mill and the spokes of a bicycle execute circular motion.

#### The displacement of a particle in simple harmonic motion is given by x=acos [ωt+ (π/3)]. The initial phase of the particle is ____.

If the displacement of a particle in simple harmonic motion is given by x = a cos (ωt + φ), then the initial phase of the particle is given by the constant in the argument of the cosine function. Hence, by comparing the given equation with the standard equation, we get the initial phase of the given particle as π/3, which is 60°.

#### Statement (i) all circular motions are periodic. Statement (ii) all periodic motions are circular.

All circular motions are periodic as they repeat after certain interval of time. But, all periodic motions are not circular. Some of them can be oscillatory, which are also periodic.

#### In damped oscillations, the mechanical energy is dissipated while doing work against the ____ forces.

In damped oscillations; the mechanical energy is dissipated while doing work against the resistive forces.

#### For a linear harmonic oscillator the magnitude of force: (i) increases with decrease in displacement (ii) obeys Newton’s second law of motion.

For a linear harmonic oscillator, the magnitude of force is directly proportional to its displacement, and hence if the displacement increases, the magnitude of the force increases. It obeys Newton’s second law of motion.

#### The law that governs the spring force is ____.

The law that governs the spring force is Hooke’s law.

#### For a linear harmonic oscillator ____.

For a linear harmonic oscillator force is directly proportional to its displacement.

#### In damped oscillations, although the energy of the system is continuously dissipated, the oscillations remain apparently periodic.

In damped oscillations, although the energy of the system is continuously dissipated, the oscillations remain apparently periodic.

#### Which of the following is an example of a translatory motion?

Motion of a train from one place to another is an example of translatory motion. The rest of the motions mentioned are periodic motions.

#### For a linear harmonic oscillator ____.

For a linear harmonic oscillator, both potential and kinetic energies are positive.

#### In damped oscillations, although the energy of the system is continuously dissipated, the oscillations remain apparently periodic.

During damped simple harmonic motion, the angular frequency of the system in motion decreases gradually.

#### A tuning fork is marked 250 Hz. What is the time period of the prongs of the tuning fork?

Time period, T=1/n

Here, n = 250 HZ

Hence, T=1/250=0.004s= 4 ms

#### A linear combination of two periodic functions is also a periodic function.

A linear combination of two periodic functions is also a periodic function.

#### Statement (i) all oscillatory motions are periodic. Statement (ii) all periodic motions are oscillatory.

All oscillatory motions are periodic as they repeat after certain interval of time. But, all periodic motions are not oscillatory. Some of them can be circular, which are also periodic.

#### If the time period of a simple pendulum is 2s, its frequency is ___ Hz.

Frequency is the reciprocal of time period. Hence, the frequency of the given pendulum is 0.5 Hz.

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