COE in SHM

Q. A particle starts SHM from the mean position $x=0$. Its amplitude is $a$ and total energy is $E$. When the particle is at a position $5\text{cm}$ from the mean position, its kinetic energy is $\frac{3E}{4}$. The value of $a$ (in $\text{cm}$) is
[Assume, The potential energy of the particle is zero at the mean position]

Q.

The following spring block systems having same mass of the block and same spring constants were stretched or compressed to different lengths (x) and released. Match the following:

1. (1)-(i), (2) - (ii), (3) - (iii)

2. (1)-(i), (2) - (i), (3) - (iii)

3. (1)-(i), (2) - (ii), (3) - (i)

4. None of these

Q.

The pulley shown in figure has a moment of inertia I about its axis and mass m. Find the time period of vertical oscillation of its centre of mass. The spring has spring constant k and the string does not slip over the pulley.

1. none of these

2. 

3. 

4. 

Q.

All the surfaces shown in figure are frictionless. The mass of the car is M, that of the block is m and the spring has spring constant k. initially, the car and the block are at rest and the spring is stretched through a length $x_0$ when the system is released. Find the time period(s) of the two simple harmonic motions.

1. 

2. None of these

3. 

4. 

Q.

A hollow sphere of radius r rolls without slipping in a hemisphere of radius 4r. Calculate the frequency of small oscillations, about point P as shown in figure.

1. 

2. 

3. 

4. None of these

Q.

Find the period of small oscillation of the bob of mass m as shown in the figure. Mass of the rod is m.

1. None of these

2. 

3. 

4. 

Q.

Consider the situation shown in figure. Show that if the blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. Calculate the time period.

1. 

2. 

3. 

4. 

Q.

The spring shown in figure is kept I a stretched position with extension $x_0$ when the system is released. Assuming the horizontal surface to be frictionless, find the frequency of oscillation.

1. 

2. 

3. 

4. 

Q.

In the system as shown, mass of the block is 1kg and spring constant is 25 $\frac{N}{m}$. The maximum kinetic energy of the block is 50J.

1. The amplitude of oscillation is 2m

2. At half of the amplitude, the kinetic energy is 37.5 J

3. At half of the amplitude, potential energy of the spring is 12.5 J

4. At half of the amplitude, potential energy of the spring is 20 J

Q. A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is $V\left(x\right)=k|x{|}^3$, where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

1. Proportional to
2. Proportional to
3. Proportional to
4. Independent of a