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

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

A

It is always in the opposite direction to velocity

B

It is proportional to the frequency of oscillation

C

It is minimum when the speed is maximum

D

It decreases as the potential energy increases

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

What is the distance covered by boat N upstream in 5 hours? Which of the following option is sufficient alone to find the answer? A) Boat M is travelling downstream with 20% more downstream speed of boat N. Speed of boat M in still water is 10% more than the speed of boat N in still water. B) Boat M and Boat N are travelling downstream with speed 33 km/hr and 40 km/hr respectively and speed of boat M is still water is 2 times the speed of stream. C) Speed of boat M in still water is 6 km/hr less then speed of boat N in still water and speed of stream is 10 km/hr. D) Speed of stream is ½ times the speed of boat N in still water and downstream speed of boat M is 44 km/hr. E) Speed of stream is 10 km/hr and ratio of upstream speed of boat M and boat N is 3 : 2 respectively.

A

Only A and B

B

Only B and C

C

Only B

D

All A, B, C and D

E

None of A, B, C and D

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

A

True

B

False

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

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

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

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

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

একটি কণা A বিস্তারে সরল ছন্দিত স্পন্দনে স্পন্দিত হচ্ছে। সাম্যাবস্থা থেকে কত দূরত্বে কণাটির বিভব শক্তি তার মোট শক্তির এক-চতুর্থাংশ হয়? (A particle is executing Simple Harmonic Motion with an amplitude A. At what displacement from the equilibrium position, is the potential energy of the particle one-fourth of its total energy?)

A

A/4

B

A/2

C

A/√2

D

A√2

A particle is executing simple harmonic motion in a line 1.0 m long. If the time of one complete vibration is 1 sec, then the maximum velocity of the particle is

A

1.00 m/sec

B

1.57 m/sec

C

3.14 m/sec

D

6.28 m/sec

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

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