Oscillations

For a simple pendulum, having time period T, the variation of kinetic energy (K.E.) with time (t) is represented by :

1. [figure]
2. [figure]
3. [figure]
4. [figure]

The sum of kinetic energy and potential energy of a simple pendulum bob is 0.02 joule. The speed of the simple pendulum bob at equilibrium position is approximately : (Consider mass of the bob = 20 g)

1. 2.0 m/s
2. 0.2 m/s
3. 14.1 m/s
4. 1.41 m/s

Savitha, a XI standard student, while conducting an experiment to determine the effective length of a simple pendulum L, notes down the data of time taken to complete 30 oscillations as 60 s and hence calculates the length of the simple pendulum as : (Take 2 = 9.8, and g = 9.8 m/s2)

1. 0.75 m
2. 1 m
3. 1.5 m
4. 2 m

A cylindrical cork of uniform density floats in a liquid of density 1. If the cork is depressed slightly and released, it oscillates harmonically with time period T. If the same cork floats in another liquid of density 2, then the similar oscillation has time period 2T. The value of 2 / 1 is:

1. 1/4
2. 4
3. 2
4. 1/2

Consider a spring-mass simple harmonic oscillator in one dimension. The mass of the particle is m kg and the spring constant is k Nm-1. At a given instant, the extension of the spring is x-meter and the speed of the particle is v ms-1. On the x - v plane, if the graph of v as a function of x is a circle, then the correct option is:

1. k = m
2. k = 1m
3. k = m
4. k = m2

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency (t) and average amplitude A(t) of the system change with time t. Which one of the following options schematically depicts these changes correctly?

1. [figure]
2. [figure]
3. [figure]
4. [figure]

Two identical point masses P and Q, suspended from two separate massless springs of spring constants k1 and k2, respectively, oscillate vertically. If their maximum speeds are the same, the ratio (AQ/AP) of the amplitude AQ of mass Q to the amplitude AP of mass P is

1. k2k1
2. k1k2
3. k2k1
4. k1k2

If x = 5 ( t + 3 ) m represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are

1. 5 cm, 2 s
2. 5 m, 2 s
3. 5 cm, 1 s
4. 5 m, 1 s

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x2 times its original time period. Then the value of x is:

1. 3
2. 2
3. 2 3
4. 4

A particle executing simple harmonic motion with amplitude A has the same potential and kinetic energies at the displacement

1. 2 A
2. A2
3. A 2
4. A 2

The two-dimensional motion of a particle, described by r = ( i + 2 j)A t is a/an: Choose the correct answer from the options given below:

1. B, C and D only
2. A, B and C only
3. A, C and D only
4. C and D only

The x-t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t = 2 s is : [figure]

1. - 28 m s-2
2. 216 m s-2
3. - 216 m s-2
4. 28 m s-2

Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is :

1. 11
2. 9
3. 10
4. 8

The restoring force of a spring with a block attached to the free end of the spring is represented by

1. [figure]
2. [figure]
3. [figure]
4. [figure]

Identify the function which represents a non-periodic motion.

1. ( t + /4)
2. e- t
3. t
4. t + t

A body is executing simple harmonic motion with frequency 'n', the frequency of its potential energy is :

1. 4n
2. n
3. 2n
4. 3n

A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is -

1. 0.628 s
2. 0.0628 s
3. 6.28 s
4. 3.14 s

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is :

1. 3 2 rad
2. 2 rad
3. zero
4. rad

The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure. [figure] y- projection of the radius vector of rotating particle P is :

1. y(t) = 4 ( t2 ), where y in m
2. y(t) = 3 ( 3 t2 ), where y in m
3. y(t) = 3 ( t2 ), where y in m
4. y(t) = -3 2 t, where y in m

Average velocity of a particle executing SHM in one complete vibration is :

1. A
2. A 22
3. A 2
4. zero

The displacement of a particle executing simple harmonic motion is given by y = A0 + A t + B t. Then the amplitude of its oscillation is given by :

1. A2 + B2
2. A + B
3. A + A2 + B2
4. A02 + (A + B)2

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m s-2 at a distance of 5 m from the mean position. The time period of oscillation is

1. 2 s
2. s
3. 2 s
4. 1 s

A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is

1. 1 : 9
2. 1 : 11
3. 1 : 14
4. 1 : 6

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is

1. 52
2. 4 5
3. 2 3
4. 5

A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is

1. 34
2. 43
3. 169
4. 916

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

1. 2
2. 2
3. 2 2

A particle is executing SHM along a straight line. Its velocities at distances x1 and x2 from the mean position are V1 and V2 respectively. Its time period is

1. 2 V12+V22x12+x22
2. 2 V12-V22x12-x22
3. 2 x12+x22V12+V22
4. 2 x22-x12V12-V22

When two displacements represented by y1 = a ( t) and y2 = b ( t) are superimposed the motion is

1. simple harmonic with amplitude a2+b2
2. simple harmonic with amplitude (a+b)2
3. not a simple harmonic
4. simple harmonic with amplitude ab

The oscillation of a body on a smooth horizontal surface is represented by the equation, X = A ( t) where X = displacement at time t = frequency of oscillation Which one of the following graphs shows correctly the variation of a with t? Here a = acceleration at time t T = time period

1. [figure]
2. [figure]
3. [figure]
4. [figure]

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

1. Circle
2. Hyperbola
3. Ellipse
4. Straight line passing through origin