A particle is performing SHM with amplitude AA and angular velocity ω.ω. The ratio of the magnitude of maximum velocity to maximum acceleration is:
1. ωω
2. 1ω1ω
3. ω2ω2
4. AωAω
The potential energy of a particle executing SHM is 2.5 J when its displacement is half of the amplitude. The total energy of the particle is:
1. 18 J
2. 10 J
3. 12 J
4. 2.5 J
Choose the incorrect statement:
1. | All SHM's have a fixed time period. |
2. | All motions having the same time period are SHM. |
3. | In SHM, the total energy is proportional to the square of the amplitude. |
4. | Phase constant of SHM depends on initial conditions. |
If a simple pendulum is suspended from the roof of a trolley which moves in the horizontal direction with an acceleration a, then the time period is given by T = 2π√lg'T = 2π√lg', where g'g' is equal to:
1. g
2. g - a
3. g + a
4. √g2 + a2√g2 + a2
In the given figure, when two identical springs are attached with a body of mass m, then oscillation frequency is f. If one spring is removed, then the frequency will become
1. f
2. 2f
3. √2f√2f
4. f√2f√2
The function sin2(ωt)sin2(ωt) represents:
1. An SHM with a period of 2πω2πω
2. An SHM with a period of πωπω
3. A periodic motion but not SHM with a period of 2πω2πω
4. A periodic motion but not SHM with a period of πωπω
Values of the acceleration A of a particle moving in simple harmonic motion as a function of its displacement x are given below
A (mms-2) 16 8 0 8 -16
x (mm) 4 -2 0 2 4
The period of the motion is :
1. 1πs
2. 2πs
3. π2s
4. πs
The acceleration-time graph of a particle undergoing SHM is shown in the figure. Then,
1. | the velocity of the particle at point 2 is zero |
2. | velocity at point 3 is zero |
3. | velocity at point 2 is +ve and maximum |
4. | both (2) & (3) |
1. | maybe K0 |
2. | must be K0 |
3. | maybe more than K0 |
4. | both (1) and (3) |
A body of mass M is situated in a potential field. The potential energy of the body is given by U(x) = U0[1 - cos Kx]; where x is position, K and U0 are constant. Period of small oscillations of the body will be:
1. 2π√MU0K2
2. 2π√MU0K2
3. 2π√U0K2M
4. 2π√U0MK2