Oscillation

Practice Questions:

Question 21: moderate

The period of a simple pendulum, whose bob is a hollow metallic sphere, is T. The period is T1 when the bob is filled with sand, T2 when it is filled with mercury and T3 when it is half filled with mercury. Which of the following is true:

1. T = T1 = T2 > T3

2. T = T1 = T3 > T

3. T > T3 > T1 = T2

4. T = T1 = T2 < T3

View Answer

In Hollow Sphere (T) , Solid Spheres ( T1 and T2) Center of mass lie at center. Where as in Half filled sphere center of mass lie below center(T3).

As length of pendulum will increase in T3. Time period is highest for it.

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Question 22: moderate

A particle is executing S.H.M., If its P.E. & K.E. is equal then the ratio of displacement & amplitude will be :

1. 1/√2

2. √2

3. 1/2

4. 3/2

View Answer

\[ K.E= \frac{1}{2}K\left(A^{2}-x^{2} \right) \]

\[ P.E= \frac{1}{2}Kx^{2} \]

\[ \frac{1}{2}K\left(A^{2}-x^{2} \right)= \frac{1}{2}Kx^{2} \]

\[ x= A/\sqrt{2} \]

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Question 23: moderate

A particle is executing linear simple harmonic motion of amplitude A. What fraction of the total energy is kinetic when the displacement is half the amplitude

1. 1/4

2. 1/2√2

3. 1/2

4. 3/4

View Answer

\[ K.E= \frac{1}{2}K\left(A^{2}-x^{2} \right) \]

\[ K.E= \frac{1}{2}K\left(A^{2}-\left( \frac{A}{2}\right)^{2} \right)= \frac{3}{8} K A^{2} \]

K.E/T.E =3/4

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Question 24: moderate

A particle of mass 0.1 kg executes SHM under a force F = (–10x) Newton. Speed of particle at mean position is 6 m/s. Then amplitude of oscillations is :

1. 0.6 m

2. 0.2 m

3. 0.4 m

4. 0.1 m

View Answer

Spring Constant K = m ω² ⇒ 10 = 0.1 ω² ⇒ ω²= 100 ⇒ ω = 10 rad/sec

Speed is maximum at mean position

Vmax= Aω

6= A × 10

A = 0.6 m

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Question 25: moderate

The potential energy of a particle executing simple harmonic motion at a distance x from the equilibrium position is proportional to :

1. √x

2. x

3. x²

4. x³

View Answer

\[ U = \frac{1}{2}kx^{2} \]

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