Kinetic Energy Formulae

Q. A body of mass 1 kg is executing simple harmonic motion. Its displacement x (in cm) at time t (in second) is given by
$x=6sin(100t+\frac{\pi }{4})$The maximum kinetic energy of the body is

1. 6 J
2. 18 J
3. 24 J
4. 36 J

Q.

What is effective mass of the spring?

Q. Force constant of a weightless spring is $16\text{N/m}$. A body of mass $1.0\text{kg}$ suspended from it is pulled down through $5\text{cm}$ from its mean position and then released. The maximum kinetic energy of the body will be

1. $2\times {10}^{-2}\text{J}$
2. $4\times {10}^{-2}\text{J}$
3. $8\times {10}^{-2}\text{J}$
4. $16\times {10}^{-2}\text{J}$

Q. A spring stretches by 0.05 m when a mass of 0.5 kg is hung from it. A body of mass 1.0 kg is attached to one of its ends, the other end being fixed to the wall. The body is pulled 0.01 m along a horizontal frictionless surface and released. What is the total energy of the oscillator. Assume the string to have negligible mass and take $g=10m{s}^{-2}$

1. 0.005 J
2. 0.05 J
3. 0.5 J
4. 5 J

Q. 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. $\frac{1}{4}$
2. $\frac{1}{2\sqrt{2}}$
3. $\frac{1}{2}$
4. $\frac{3}{4}$

Q. A particle executes SHM, at what value of displacement are the kinetic and potential energies equal ?

1. $\sqrt{2}A$
2. $\frac{A}{\sqrt{2}}$
3. $\sqrt{\frac{3}{2}}A$
4. $\sqrt{\frac{2}{3}}A$

Q. For an object executing SHM, kinetic energy 'K' becomes zero when amplitude become to the maximum amplitude.

1. equal to
2. less than
3. greater than

Q.

A particle executes S.H.M (a) What fraction of total energy is kinetic? What fraction is potential when displacement is one half of the amplitude?

1. $\frac{3}{4}$ and $\frac{1}{4}$

2. $\frac{2}{3}$ and $\frac{1}{3}$

3. $\frac{1}{2}$ and $\frac{1}{2}$

4. $\frac{1}{6}$ and $\frac{5}{6}$

Q.

Starting from the mean position a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy ?

1. $\left(\frac{1}{6}\right)$s

2. $\left(\frac{1}{4}\right)$s

3. $\left(\frac{1}{3}\right)$s

4. $\left(\frac{1}{12}\right)$s

Q. The total energy of a particle performing $\text{SHM}$ is $E$. What will be the kinetic energy of the particle, when displacement is half of the amplitude?

1. $\frac{\sqrt{3}}{2}E$
2. $\frac{E}{2}$
3. $\frac{3E}{4}$
4. $\frac{E}{3}$

Q.

A loaded vertical spring executes simple harmonic oscillations with period of 4 s. The difference between the kinetic energy and potential energy of this system oscillates with a period of

1. 8 s

2. 1 s

3. 2 s

4. 4 s

Q. Two bodies A and B of equal masses are suspended from two separate springs of force constants $k_{1}and{k}_2$ respectively. If the two bodies oscillate such that their maximum velocities are equal, the ratio of the amplitudes of oscillation of A and B will be

1. $\frac{k_1}{k_2}$
2. $\sqrt{\frac{k_1}{k_2}}$
3. $\frac{k_2}{k_1}$
4. $\sqrt{\frac{k_2}{k_1}}$

Q. A spring block system is put into $\text{SHM}$ in two experiments. In the first experiment, the block is pulled from the equilibrium position through a distance $d_1$ and then released. In the second experiment, it is pulled from the equilibrium position through a greater distance $d_2$ and then released. For the given scenario choose the incorrect statement.

1. Time period is same for both $\text{SHM}$
2. Frequency is same for both $\text{SHM}$
3. Maximum kinetic energy is same for both $\text{SHM}$
4. Angular frequency is same for both $\text{SHM}$

Q. A body of mass $2\text{kg}$ is executing simple harmonic motion. Its displacement $y\text{(in cm)}$ at $t$ seconds is given by $y=6\sin (200t+\frac{\pi }{6})$. Find its maximum kinetic energy.

1. $144\text{kJ}$
2. $12\text{J}$
3. $48\text{kJ}$
4. $144\text{J}$

Q. A particle of mass $0.3\text{kg}$ executes SHM with an amplitude $0.06\text{m}$ and frequency $10$ vibrations/sec. Find its total energy of oscillation.

1. $5\text{J}$
2. $2.13\text{J}$
3. $3\text{J}$
4. $8.5\text{J}$

Q. The total energy of a particle performing $\text{SHM}$ is $E$. What will be the kinetic energy of the particle, when displacement is half of the amplitude?

1. $\frac{\sqrt{3}}{2}E$
2. $\frac{E}{2}$
3. $\frac{3E}{4}$
4. $\frac{E}{3}$

Q. The total vibrational energy of a particle in $\text{SHM}$ is $E$. Its kinetic energy at half the amplitude from mean position will be :

1. $E/2$
2. $E/3$
3. $E/4$
4. $3E/4$