# When the displacement is half the amplitude in an SHM, the ratio of potential energy to the total energy is: 1. $$\frac{1}{2}$$ 2. $$\frac{1}{4}$$ 3. $$1$$ 4. $$\frac{1}{8}$$

Subtopic:  Energy of SHM |
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A block is connected to a relaxed spring and kept on a smooth floor. The block is given a velocity towards the right. Just after this:

 1 the speed of block starts decreasing but acceleration starts increasing. 2 the speed of the block as well as its acceleration starts decreasing. 3 the speed of the block starts increasing but its acceleration starts decreasing. 4 the speed of the block as well as acceleration start increasing.

Subtopic:  Spring mass system |
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A mass m is suspended from two springs of spring constant ${k}_{1}$ $and$ ${k}_{2}$ as shown in the figure below. The time period of vertical oscillations of the mass will be

1. $2\mathrm{\pi }\sqrt{\left(\frac{{\mathrm{k}}_{1}+{\mathrm{k}}_{2}}{\mathrm{m}}\right)}$

2. $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\left({\mathrm{k}}_{1}+{\mathrm{k}}_{2}\right)}}$

3. $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}\left({\mathrm{k}}_{1}{\mathrm{k}}_{2}\right)}{\left({\mathrm{k}}_{1}+{\mathrm{k}}_{2}\right)}}$

4. $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}\left({\mathrm{k}}_{1}+{\mathrm{k}}_{2}\right)}{\left({\mathrm{k}}_{1}{\mathrm{k}}_{2}\right)}}$

Subtopic:  Combination of Springs |
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One end of a spring of force constant $$k$$ is fixed to a vertical wall and the other to a block of mass $$m$$ resting on a smooth horizontal surface. There is another wall at a distance $$x_0$$ from the block. The spring is then compressed by $$2x_0$$ and then released. The time taken to strike the wall will be?

 1 $$\frac{1}{6} \pi \sqrt{ \frac{k}{m}}$$ 2 $$\sqrt{\frac{k}{m}}$$ 3 $$\frac{2\pi}{3} \sqrt{ \frac{m}{k}}$$ 4 $$\frac{\pi}{4} \sqrt{ \frac{k}{m}}$$
Subtopic:  Spring mass system |
72%
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In simple harmonic motion, the ratio of acceleration of the particle to its displacement at any time is a measure of:
 1 Spring constant 2 Angular frequency 3 (Angular frequency)2 4 Restoring force
Subtopic:  Simple Harmonic Motion |
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The amplitude and the time period in an SHM are $$0.5$$ cm and $$0.4$$ sec respectively. If the initial phase is $$\frac{\pi}{2}$$ radian, then the equation of SHM will be:
1. $$y = 0.5\sin(5\pi t)$$
2. $$y = 0.5\sin(4\pi t)$$
3. $$y = 0.5\sin(2.5\pi t)$$
4. $$y = 0.5\cos(5\pi t)$$
Subtopic:  Linear SHM |
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The angular velocities of three bodies in simple harmonic motion are $$\omega_1, \omega_2, \omega_3$$ with their respective amplitudes as $$A_1, A_2, A_3.$$ If all the three bodies have the same mass and maximum velocity, then:
 1 $$A_1 \omega_1=A_2 \omega_2=A_3 \omega_3$$ 2 $$A_1 \omega_1^2=A_2 \omega_2^2=A_3 \omega_3^2$$ 3 $$A_1^2 \omega_1=A_2^2 \omega_2=A_3^2 \omega_3$$ 4 $$A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2$$
Subtopic:  Simple Harmonic Motion |
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The total energy of a particle, executing simple harmonic motion is:
1. $$\propto x$$
2. $$\propto x^2$$
3. Independent of $$x$$
4. $$\propto x^{\frac{1}{2}}$$
Subtopic:  Energy of SHM |
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A body is executing simple harmonic motion. At a displacement $$x,$$ its potential energy is $$E_1$$ and at a displacement $$y$$, its potential energy is $$E_2$$${}_{}$. The potential energy $$E$$ at displacement $$x+y$$ will be?
1. $$E = \sqrt{E_1}+\sqrt{E_2}$$
2. $$\sqrt{E} = \sqrt{E_1}+\sqrt{E_2}$$
3. $$E =E_1 +E_2$$
4. None of the above

Subtopic:  Energy of SHM |
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The equation of motion of a particle is $${d^2y \over dt^2}+Ky=0$$ where $$K$$ is a positive constant. The time period of the motion is given by:
 1 $$2 \pi \over K$$ 2 $$2 \pi K$$ 3 $$2 \pi \over \sqrt{K}$$ 4 $$2 \pi \sqrt{K}$$
Subtopic:  Simple Harmonic Motion |
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