A particle is executing simple harmonic motion at midpoint of mean position and extremely. What is the potential energy in terms of total energy (E)?

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

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

The particle executing simple harmonic motion has a kinetic energy K0 cos2 ωt. The maximum values of the potential energy and the total energy are respectively ___________

A

Kc/2 and K0

B

K0 and K0

C

K0 and 2K0

D

0 and 2K0

A square ABCD, L is the midpoint of side AB, M is the midpoint of side BC, N is the midpoint of side CD and O is the midpoint of side AD, then find the ratio of area of shaded region PQRS to the area of square ABCD.

A

1 ∶ 4

B

1 ∶ 5

C

1 ∶ 6

D

1 ∶ 8

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

A

True

B

False

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}} $

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

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

If A is the amplitude of particle executing simple harmonic motion, then the total energy E of the particle is

A

Proportional to A

B

Proportional to A²

C

Proportional to $$\frac{1}{{{{\text{A}}^2}}}$$

D

Independent of A

A particle is executing simple harmonic motion of amplitude 10cm. Its time period of oscillation is π seconds. The velocity of the particle when it is 2 cm from extreme position is ___________

A

10 cm/s

B

12 cm/s

C

16√16 cm/s

D

16 cm/s

A particle executes simple harmonic motion of amplitude A. At what distance from the mean position is its kinetic energy equal to its potential energy?

A

0.51A

B

0.71A

C

0.61A

D

0.81A

A particle is executing simple harmonic motion at midpoint of mean position and extremely. What is the potential energy in terms of total energy (E)?

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