A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true?

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

A

True

B

False

Which one of the following statements is true for the speed v and the acceleration of a particle executing simple harmonic motion?

A

When c is maximum, a is maximum

B

Value of a is zero, whatever may be the value of v

C

When v is zero, a is zero

D

When v is maximum, a is zero

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 executing simple harmonic motion has amplitude 0.01 and frequency 60Hz. The maximum acceleration of the particle is ___________

A

144 π2 m/s2

B

80 π2 m/s2

C

120 π2 m/s2

D

60 π2 m/s2

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

If the equation of motion of a particle moving along the y-axis is y = P + Q sin ωt, the particle must be executing simple harmonic motion with amplitude

A

P

B

Q

C

P + Q

D

\(\sqrt {{P^2} + {Q^2}} \)

Statement: In simple harmonic motion, the velocity is maximum, when the acceleration is minimum. Reason: Displacement and velocity in simple harmonic motion is differ in phase by π/2.

A

Both statement and reason are true and the reason is the correct explanation of the statement

B

Both statement and reason are true but the reason is not the correct explanation of the statement

C

Statement is true, but the reason is false

D

Statement and reason are false

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

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

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is ___________

A

0.5π

B

π

C

0.707 π

D

0.61 π

A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true?

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