### Physics - Oscillations and Waves

#### Question - 1

An elestic ball is dropped from a certain height and return to the same height after elastic collision on the flloor.  What is the nature of repeated motion of the ball?

• A Simple harmonic, oscillatory and periodic
• B Simple harmonic, oscillatory but not periodic
• C Simple harmonic,periodic but not oscillatory
• D oscillatory,periodic but not simple harmonic

#### Question - 2

The graph between restoring force and time in case of SHM is

• A a straight line
• B a circle
• C a parabola
• D a sine curve

#### Question - 3

The displacement of SHM is given by y = 5 cos (10t+0.6), What is the initial phase os SHM?

• D None of these

#### Question - 4

A sysytem is subjected to two SHMs given by ${ y }_{ 1 }^{ }$ = 6 cos $\omega$ t and ${ y }_{ 2 }^{ }$ = 8 cos $\omega$ t, The resultant amplitude of SHM is given by

• A 2
• B 10
• C 14
• D 20

#### Question - 5

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is neglible. When pressed slighty and released the mass executes a simple harmonic motion. the spring constant is 200${ Nm }_{ }^{ -1 }$ . What should be the minimum amplitude of the motion, so that the mass gets detached from the pan?

• A 8.0 cm
• B 10.0 cm
• C Any value less than 12.0 cm
• D 4.0 cm

#### Question - 6

The displacement of a particle varies with time according to the relation y = a sin $\omega$ t + b cos $\omega$ t.

• A The motion is oscillatory but not SHM
• B The motion is SHM with amplitude a + b
• C The motion is SHM with amplitude ${ a }_{ }^{ 2 }+{ b }_{ }^{ 2 }$
• D The motion is SHM with amplitude $\sqrt { { a }_{ }^{ 2 }+{ b }_{ }^{ 2 } }$

#### Question - 7

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

• A $\frac { T }{ 4 }$
• B $\frac { T }{ 8 }$
• C $\frac { T }{ 12 }$
• D $\frac { T }{ 16 }$

#### Question - 8

A particle executes SHM with a period of T second and amplitude A metre. The shorstest time it takes to reach point $\frac { A }{ \sqrt { 2 } }$ metre from its mean position in second is

• A T
• B $\frac { T }{ 4 }$
• C $\frac { T }{ 8 }$
• D $\frac { T }{ 16 }$

#### Question - 9

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 haramonic motion of the X- projection of the radius vector of the rotating particle P is

• A $x=2\cos { \left( 2\pi +\cfrac { \pi }{ 4 } \right) }$
• B $x=2\sin { \left( 2\pi t+\cfrac { \pi }{ 4 } \right) }$
• C $x=2\sin { \left( 2\pi t-\cfrac { \pi }{ 4 } \right) }$
• D $x=2\cos { \left( 2\pi t-\cfrac { \pi }{ 4 } \right) }$

#### Question - 10

The equation of two linear SHM's are

X = a sin $\omega t$, along X-axis

Y = a sin2 $\omega t$, along Y-axis If they act on a particle simultaneously, the trajectory of the particle is

• A $\frac { { y }^{ 2 } }{ { a }^{ 2 } } +\frac { { x }^{ 2 } }{ { 4a }^{ 2 } }$= 1
• B ${ y }^{ 2 }=\quad \frac { 4{ x }^{ 2 } }{ { a }^{ 2 } }$${ (a }_{ }^{ 2 }-{ x }^{ 2 })$
• C ${ y }^{ 2 }=$ 2ax
• D None of these