If the kinetic energy and potential energy of a simple harmonic oscillator of amplitude A are both equal to half the total energy, then the displacement is equal to

The ratio of kinetic energy and potential energy of a simple harmonic oscillator, at a displacement equal to half its amplitude is given by

A

1 : 2

B

1 : 1

C

2 : 1

D

3 : 1

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

সরল দোল গতিসম্পন্ন একটি বস্তু যখন তার সাম্যাবস্থান থেকে 2 cm দূরে, তখন তার গতিশক্তি স্থিতিশক্তির ও গুণ। বস্তুটির দোলনের বিস্তার কত হবে? (An object oscillating in simple harmonic motion has its kinetic energy 3 times the potential energy when the object is 2 cm away from its equilibrium position. What is the amplitude of the oscillation for the object?)

A

3 cm

B

1 cm

C

2 cm

D

4 cm

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

Overmodulation (amplitude) occurs when signal amplitude is ___________ carrier amplitude

A

Equal to

B

Greater than

C

Less than

D

None of the above

A man sells chocolates which are in the boxes. Only either full box or half a box of chocolates can be purchased from him. A customer comes and buys half the number of boxes which the seller had plus half box more. A second customer comes and purchases half the remaining number of boxes plus half a box. After this the seller is left with no chocolate boxes. How many chocolate boxes the seller had initially?

A

2

B

3

C

4

D

3.5

E

None of these

একটি সরল দোলকের সুতার দৈর্ঘ্য 99 cm এবং এর দোলনকাল 2 sec হলে দোলক পিন্ডের ব্যাসার্ধ নির্ণয় কর। (The length of the string and period of oscillation of a simple oscillator are 99 cm and 2 sec, respectively. Find the radius of the oscillator.)

A

1.29 cm

B

7 mm

C

3.18 mm

D

0.28 cm

E

2.15 mm

সরল ছন্দিত স্পন্দন ( simple harmonic oscillator)- এর ক্ষেত্রে কোনটি সঠিক সমীকরণ?

A

d2xdy2+w2x=0

B

d2xdy2+w2y=0

C

d2xdt2+w2t=0

D

d2xdt2+ ϖ2x=0

সরল দোল গতি (simple harmonic motion ) সম্পন্ন কোন বস্তুর সর্বোচ্চ গতিশক্তি (maximum kinetic energy ) -র সমীকরণ -

A

(Ek)max=12mϖ2a2

B

(Ek)max=12mϖ2k2

C

(Ek)max=12mϖa2

D

(Ek)=12mϖK2

If the kinetic energy and potential energy of a simple harmonic oscillator of amplitude A are both equal to half the total energy, then the displacement is equal to

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