STANDARD Physics Oscillations Class 11 Questions

Out of the following representing motion of a particle which represents SHM? 1. x = sin³ωt 2. x = 1 + ωt + ω²t² 3. x = cosωt + cos3ωt + cos5ωt 4. x = sinωt + cosωt

Which of the following is not a characteristic of simple harmonic motion?

If a simple harmonic motion is represented by \( \frac{d^2x}{dt^2} + cx = 0 \), its time period is

If x, v and a represent the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T then which of the following does not change with time?

Two simple harmonic motions are represented by the equations, \( y_1 = 10\sin\left(\frac{\pi}{4}(12t + 1)\right) \), \( y_2 = 5(\sin 3\pi t + \sqrt{3}\cos 3\pi t) \). The ratio of their amplitudes is

In an experiment, the period of oscillation of a simple pendulum was observed to be 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s. The mean absolute error is

The displacement-time graph for a particle executing SHM is as shown in figure. Which of the following statements is correct?

Displacement versus time curve for a particle executing SHM is as shown in figure. At what points the velocity of the particle is zero?

A particle executing SHM with time period T and amplitude A. The mean velocity of the particle averaged over quarter oscillation is

A particle executing SHM. The phase difference between velocity and displacement is

The period of oscillation of a simple pendulum is T = 2π√(L/g). Measured value of L is 10 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 50 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g?

A particle is in linear simple harmonic motion between two points A and B, 10 cm apart (figure). Take the direction from A to B as the +ve direction. Which of the following statements is correct?

A particle executing SHM. The phase difference between acceleration and displacement is

A particle executing SHM according to the equation x = 5cos(2πt + π/4) in SI units. The displacement and acceleration of the particle at t = 1.5 s is

The x-t graph of a particle undergoing simple harmonic motion is as shown in the figure. The acceleration of the particle at t = 4/3 s is

As the temperature is increased, the time period of a pendulum

A particle executing simple harmonic motion with an amplitude 5 cm and a time period 0.2 s. The velocity and acceleration of the particle when the displacement is 5 cm is

In simple harmonic motion, at the extreme positions

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T = 0°C. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α, then the value of S is

The displacement of a particle executing simple harmonic motion is given by x = 3 sin(2πt + π/4) where x is in metres and t is in seconds. The amplitude and maximum speed of the particle is

A particle of mass m executing SHM with amplitude A and angular frequency ω. The average value of the kinetic energy and potential energy over a period is

A block of mass m hanging vertically by spring of spring constant k. If the mass is made to oscillate vertically, its total energy is

Frequency of variation of kinetic energy of a simple harmonic motion of frequency n is

A particle executing SHM with an amplitude A. The displacement of the particle when energy is half of its total energy is

For a particle executing simple harmonic motion the displacement x is given by x = A cos ωt. Identify the graph, which represents the variation of potential energy (U) as a function of time t and displacement x.

When the displacement of a particle executing SHM is one-fourth of its amplitude, what fraction of the total energy is the kinetic energy?

The frequency of oscillations of a mass m suspended by a spring is v₁. If the length of the spring is cut to one-half, the same mass oscillates with frequency v₂. The value v₂/v₁ is

Time period of oscillation of a spring is 12 s on Earth. What shall be the time period if it is taken to moon?

A body of mass 20 g connected to a spring of spring constant k, executes simple harmonic motion with a frequency of (5/π) Hz. The value of spring constant is

A trolley of mass 3 kg, as shown in figure, is connected to two identical springs, each of spring constant 600 N m⁻¹. If the trolley is displaced from its equilibrium position by 5 cm and released, the maximum speed of the trolley is

What is the effect on the time period of a simple pendulum if the mass of the bob is doubled?

Match the column I with column II.

A simple pendulum suspended from roof of a lift oscillates with frequency v when the lift is at rest. If the lift falls freely under gravity, its frequency of oscillation becomes

A rectangular block of mass m and area of cross-section floats in a liquid of density ρ. If is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T. Then

The displacement of a particle is represented by the equation y = 3 cos(π/4 - 2ωt). The motion of the particle is

The displacement of a particle is represented by the equation y = sin³ ωt. The motion is

The relation between acceleration and displacement of four particles are given below: Which one of the particles is executing simple harmonic motion?

A particle is acted simultaneously by mutually perpendicular simple harmonic motions x = a cos ωt and y = a sin ωt. The trajectory of motion of the particle will be

The displacement of a particle varies with time according to the relation y = a sin ωt + b cos ωt.

When a mass m is connected individually to two springs S₁ and S₂, the oscillation frequencies are v₁ and v₂. If the same mass is attached to the two springs as shown in figure, the oscillation frequency would be

Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is

Assertion: The graph of total energy of a particle in SHM with respect to position is a straight line with zero slope. Reason: Total energy of particle in SHM remains constant throughout its motion.

A particle executes simple harmonic motion between x = -A and x = +A. The time taken for it to go from 0 to A/2 is T₁ and to go from A/2 to A is T₂. Then

Starting from the origin, a body oscillates simple harmonically with a period of 2s. After what time will its kinetic energy be 75% of the total energy?

A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then, its time period of vibration will be

A particle is performing simple harmonic motion with angular frequency 5000 radian/second and amplitude 2 cm and mass of 1 kg. Find the total energy of oscillation.

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration.

A simple harmonic motion is represented by y = 5(sin3πt + √3 cos3πt) cm. The amplitude and time period of the motion are

Assertion: In simple harmonic motion, kinetic energy and potential energy become equal when the displacement is (1/√2) times the amplitude. Reason: In simple harmonic motion, kinetic energy is zero when potential energy is maximum.

A body of mass 5 kg is executing simple harmonic motion with amplitude 5 m and frequency ω = rad/sec when it is 1 m away from mean position, what will be the kinetic energy and potential energy acquired by the body?