Oscillations

Q. When the body is in a stable equilibrium position, it will have least​​​​​ potential energy.

1. True
2. False

Q. Which of the following statement is incorrect for a particle performing linear SHM?

1. Acceleration is always directed opposite to the direction of displacement.
2. Velocity of the particle is constant.
3. The net force on the particle is zero at mean position.
4. Acceleration is proportional to the displacement from mean position.

Q.

A particle moves in a potential region given by $U=8x^2-4x+400$. Its state of equilibrium will be

1. $0.25M$

2. $8M$

3. $10M$

4. $12M$

Q. For the given oscillatory motion, $F=-k(x-b{)}^3$, find out the mean position of the particle.

1. $x=-b$
2. $x=+b$
3. $x=0$
4. $x=\frac{b}{2}$

Q. All oscillatory motions are periodic also.

1. False
2. True

Q. When the body is in a stable equilibrium position, it will have least​​​​​ potential energy.

1. True
2. False

Q. Which of the following expressions represents an oscillatory motion ?

1. $F=-2(x-2{)}^3$
2. $F=-2(x-2{)}^2$
3. $F=2(x-2{)}^3$
4. $F=2(x-2{)}^2$

Q. A particle starts from mean position ${}^{\prime }{O}^{\prime }$ where $x=0$ and oscillates to and fro about this point. When it is passing through ${}^{\prime }{O}^{\prime }$ while moving towards negative extreme position , find the phase constant $\varphi$ of the particle at this point.

1. $\varphi =0^{\circ }$
2. $\varphi =\frac{\pi }{2}$
3. $\varphi =\pi$
4. $\varphi =\frac{\pi }{4}$

Q. While a particle executes simple harmonic motion, the rate of change of acceleration is maximum and minimum, respectively at:

1. The mean position and extreme positions
2. The extreme positions and mean position
3. The mean position alternatively.
4. The extreme positions alternatively.

Q. The density $\rho$ of a liquid varies with depth $h$ from the free surface as $\rho =kh$. A small body of density ${\rho }_1$ is released from the surface of the liquid. The body executes $SHM$ with amplitude

1. $\frac{2{\rho }_1}{k}$
2. $\frac{{\rho }_1}{k}$
3. $\frac{\sqrt{2}{\rho }_1}{k}$
4. $\frac{\sqrt{3}{\rho }_1}{k}$

Q. All oscillatory motions are periodic also.

1. False
2. True