Oscillations

The time period of a simple pendulum in a lift descending with constant acceleration g is

A spring has time period T. It is cut into n equal parts. The time period of each part will be

The velocity of a particle performing simple harmonic motion, when it passes through its mean position is

Acceleration of a particle, executing SHM, at its mean position is

When a mass M is attached to a spring of force constant K, then the spring stretches by l. If the mass oscillates with amplitude l, what will be maximum potential energy stored in the spring

The time period of a mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

A particle is executing the motion x = A cos (ωt-θ). The maximum velocity of the particle is

The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where E is the total energy)

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is

A thin wire of length L and mass M is bent to form a semicircle. What is the gravitational field at the centre?

The particle executing simple harmonic motion has a kinetic energy K₀ cos²ωt. The maximum values of the potential energy and the total energy are respectively

A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

A point performs simple harmonic oscillation of period T and the equation of motion is given by x=a sin(ωt+π/6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

A particle of mass M is executing oscillations about the origin on the x-axis. The potential energy is U(x)=k|x|³, where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

The total energy of a simple harmonic oscillator is proportional to

For a simple pendulum performing simple harmonic motion, the time period is plotted against its length. The curve will be

Two simple harmonic motions of angular frequency 100 and 1000 rad s⁻¹ have the same displacement amplitude. The ratio of other maximum accelerations is:

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x = a/2 will be:

Which one of the following equations of motion represents simple harmonic motion?

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be:

The displacement of a particle along the x-axis is given by x = a sin² ωt. The motion of the particle corresponds is:

The period of oscillation of a mass M suspended from a spring of negligible mass is T. If along with it another mass M is also suspended, the period of oscillation will now be

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:

A particle of mass m oscillates along x-axis according to equation x = a sin ωt. The nature of the graph between momentum and displacement of a particle is