In linear simple harmonic motion of a particle at mean position:

Every simple harmonic motion is periodic motion, but every periodic motion need not be simple harmonic motion.

A

True

B

False

Which of the following is/are the characteristics of simple harmonic motion (i) The total energy is conserved (ii) The acceleration is directly proportional to the displacement and is directed towards its mean position (iii) The simple harmonic motion cannot be represented using sinusoidal functions (iv) There are a maximum and minimum displacement about the equilibrium point

A

All the options

B

(i), (ii) and (iii)

C

(i), (ii) & (iv)

D

(i), (iii) & (iv) only

A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is

A

1/ 2π√3

B

2π√3

C

2π/√3

D

√3/2π

The velocity of a particle (v) moving with simple harmonic motion, at any instant is given by (where, r = Amplitude of motion and y = Displacement of the particle from mean position.)

A

$$\omega \sqrt {{{\text{y}}^2} - {{\text{r}}^2}} $$

B

$$\omega \sqrt {{{\text{r}}^2} - {{\text{y}}^2}} $$

C

$${\omega ^2}\sqrt {{{\text{y}}^2} - {{\text{r}}^2}} $$

D

$${\omega ^2}\sqrt {{{\text{r}}^2} - {{\text{y}}^2}} $$

A particle in uniform circular motion is projected on its diameter. The motion of projection will be simple harmonic. Select the correct option regarding speed and acceleration of the particle in circular motion.

A

Speed is constant, acceleration is zero

B

Speed is constant, acceleration is non-zero

C

Speed changes, acceleration is non-zero

D

Speed changes, acceleration is zero

A particle in simple harmonic motion is described by the displacement function x(t)=Acos⁡(ωt+θ). If the initial (t=0) position of the particle is 1cm and its initial velocity isπcm/s, what is its amplitude? The angular frequency is the particle is πrad/s.

A

1 cm

B

√2 cm

C

2 cm

D

2.5 cm

Match the following Types of mechanism Motion achieved P. Scott Russel mechanism 1. Intermittent motion Q. Geneva mechanism 2. Quick return motion R. Off set slider crank mechanism 3. Simple harmonic motion S. scotch Yoke mechanism 4. Straight line motion

A

P-2,Q-3,R-1,S-4

B

P-3,Q-2,R-4,S-1

C

P-4,Q-1,R-2,S-3

D

P-4,Q-3,R-1,S-2

The velocity of a particle moving with simple harmonic motion, at any instant is given by (where $$\omega $$ = Displacement of the particle from mean position)

A

$$\omega \sqrt {{{\text{x}}^2} - {{\text{r}}^2}} $$

B

$$\omega \sqrt {{{\text{r}}^2} - {{\text{x}}^2}} $$

C

$${\omega ^2}\sqrt {{{\text{x}}^2} - {{\text{r}}^2}} $$

D

$${\omega ^2}\sqrt {{{\text{r}}^2} - {{\text{x}}^2}} $$

The acceleration of the particle moving with simple harmonic motion is inversely proportional to the displacement of the particle from the mean position.

A

True

B

False

Consider the following types of motion. A. Periodic Motion B. Straight Line Motion C. Rotational Motion D. Circular Motion The motion of a pendulum can be categorised in which of the following types of motion?

A

A, D

B

B and C

C

A

D

A, D, C

In linear simple harmonic motion of a particle at mean position:

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