In a simple harmonic oscillation, the acceleration against displacement for one complete oscillation will be

(a)

an ellipse

(b)

a circle

(c)

a parabola

(d)

a straight line

The length of a second’s pendulum on the surface of the Earth is 0.9 m. The length of the same pendulum on surface of planet X such that the acceleration of the planet X is n times greater than the Earth is

(a)

0.9n

(b)

\(\frac{0.9}{n}\)m

(c)

0.9n²m

(d)

\(\frac{0.9}{n^2}\)

The time period for small vertical oscillations of block of mass m when the masses of the pulleys are negligible and spring constant k₁ and k₂ is

(a)

\(T=4\pi \sqrt { m\left( \frac { 1 }{ { k }_{ 1 } } +\frac { 1 }{ { k }_{ 2 } } \right) } \)

(b)

\(T=2\pi \sqrt { m\left( \frac { 1 }{ { k }_{ 1 } } +\frac { 1 }{ { k }_{ 2 } } \right) } \)

(c)

\(T=4\pi \sqrt { m\left( { k }_{ 1 }+{ k }_{ 2 } \right) } \)

(d)

\(T=2\pi \sqrt { m\left( { k }_{ 1 }+{ k }_{ 2 } \right) } \)

An ideal spring of spring constant k, is suspended from the ceiling of a room and a block of mass M is fastened to its lower end. If the block is released when the spring is un-stretched, then the maximum extension in the spring is

(a)

4\(\frac { Mg }{ k } \)

(b)

\(\frac { Mg }{ k } \)

(c)

2\(\frac { Mg }{ k } \)

(d)

\(\frac { Mg }{ 2k } \)

A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will

(a)

first increase and then decrease

(b)

first decrease and then increase

(c)

increase continuously

(d)

decrease continuously

When a damped harmonic oscillator completes 100 oscillations, its amplitude is reduced to \(\frac{1}{3}\) of its initial value. What will be its amplitude when it completes 200 oscillations?

(a)

\(\frac{1}{5}\)

(b)

\(\frac{2}{3}\)

(c)

\(\frac{1}{6}\)

(d)

\(\frac{1}{9}\)

A particle excites simple harmonic motion between x = -A & x = +A, the time taken for it to go from 0 to \(\frac{A}{2}\) is T₁ & to go from \(\frac{A}{2}\) to A is T₂ then _______________.

(a)

T₁2

(b)

T₁>T₂

(c)

T₁=T₂

(d)

T₁=2T₂

The simple harmonic motions are respresented by the equation. y₁ = 0.1 sin (100πt + π/3) & Y₂= 0.1 cos π the phase difference of the velocity of particle is _________________.

(a)

-\(\frac { \pi }{ 6 } \)

(b)

\(\frac { \pi }{ 3 } \)

(c)

-\(\frac { \pi }{ 6 } \)

(d)

\(\frac { \pi }{ 6 } \)

The man velocity of a particle, executing simple harmonic motion with an amplitude 7 mm is 4.4 m s^-1. The period of oscillation is ________________.

(a)

0.01s

(b)

0.1s

(c)

10s

(d)

100s

A particle executing simple harmonic motion along y-axis has its motion described by the equation y = A.sin (ωt) + B, the amplitude of the example harmonic motion is ______________.

(a)

A

(b)

B

(c)

A+B

(d)

\(\sqrt{A+B}\)

A particle is executing SHM at mid point of mean position & extermity. What is the potential energy in terms of total energy (E) _______________.

(a)

\(\frac{E}{4}\)

(b)

\(\frac{E}{16}\)

(c)

\(\frac{E}{2}\)

(d)

\(\frac{C}{8}\)

What is time period of a pendulum hanged in a satellite? (T is time period on earth)

(a)

zero

(b)

T

(c)

infinite

(d)

\(\frac { T }{ \sqrt { 6 } } \)

The magnitude of acceleration of particle executing SHM at the position of maximum displacement is ____________.

(a)

zero

(b)

minimum

(c)

maxmium

(d)

none of these

Find the length of a simple pendulum whose period is 2.00 s _______________.

(a)

2 m

(b)

0.4 m

(c)

0.1 m

(d)

3 m

The three springs with force constant \({ k }_{ 1 }=7.5\frac { N }{ m } ,{ k }_{ 2 }=10.0\frac { N }{ m } ,{ k }_{ 3 }=12.5\frac { N }{ m } \), are connected in parallel to a mass of 0.500 kg. The mass is then pulled to the right and released. Then the period of the motion is _______________.

(a)

0.6s

(b)

0.8s

(c)

0.5 s

(d)

004 s

A particle executing a SHM has a maximum displacement of 2 cm its acceleration at a distance of 0.5 cm from its mean position is 2 cm/s², What will be its velocity when it is at a distance of 1 cm from its mean position?

(a)

4 cm/s

(b)

2\(\sqrt{3}\)

(c)

11.2 cm/s

(d)

4\(\sqrt{7}\)

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with S.H.M with an angular frequency of 200 rad/min. Then the maximum speed will be _________.

(a)

50 m/min

(b)

100 m/min

(c)

150 m/min

(d)

200 m/min

A small body of mass 50 g is undergoing SHM of amplitude 100 cm and period 0.2 s. What is the maximum value of the force acting on the body?

(a)

86.4 N

(b)

98.5 N

(c)

102.1 N

(d)

71.2 N

In order to double the period of a simple pendulum _______.

(a)

its length should doubled

(b)

its length should be quadrupled

(c)

the mass of its bob should be doubled

(d)

the mass of its bob should be quadrupled.

A particle is executing SHM. Then the graph of velocity as a function of displacement is _______.

(a)

straight line

(b)

circle

(c)

ellipse

(d)

hyperbola