Oscillations

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