Oscillations

The velocity of a particle executing simple harmonic motion along x-axis is described as v2=50-x2, where x represents displacement. If the time period of motion is x7 s, the value of x is .

The displacement of a particle, executing simple harmonic motion with time period T, is expressed as x(t) = A t, where A is the amplitude. The maximum value of potential energy of this oscillator is found at t = T/2 . The value of is .

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m, 2 ms-1 and 16 ms-2 at a certain instant. The amplitude of the motion is x m where x is .

A particle of mass 0.50 kg executes simple harmonic motion under force F = -50( Nm-1)x. The time period of oscillation is x35 s. The value of x is . (Given = 227)

An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of ( 25 )Hz. At the position x = 0.04 m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is cm.

A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is cm/s.

The displacement of a particle executing SHM is given by x = 10 ( t + 3 ) m. The time period of motion is 3.14 s. The velocity of the particle at t = 0 is m/s.

A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency f1. The frequency of oscillations if a mass 9 m is suspended from the same spring is f2. The value of f1f2 is .

A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is 2A3. The new amplitude of motion is nA3. The value of n is .

The time period of simple harmonic motion of mass M in the given figure is M5k, where the value of is . [figure]

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillations will be s. [take g= 2 m s-2]

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is x8, where x= .

A simple harmonic oscillator has an amplitude A and time period 6 second. Assuming the oscillation starts from its mean position, the time required by it to travel from x=A to x= 32 A will be x s, where x= .

A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean position, velocity of the particle is 10 cm/s. The distance of the particle from the mean position when its speed becomes 5 cm/s is cm, where = .