For a particle executing SHM the displacement \(x \) is given by, \(A\cos \omega t.\) Identify the graph which represents the variation of potential energy (P.E.) as a function of time \(t\) and displacement \(x.\)
1. I, III
2. II, IV
3. II, III
4. I, IV
The variation of acceleration, \(a~\) of a particle executing SHM with displacement \(x~\) is:
1. | 2. | ||
3. | 4. |
The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
1. 25 Hz
2. 50 Hz
3. 12.25 Hz
4. 33.3 Hz
The displacement-time graph of a particle executing SHM is shown in the figure. Its displacement equation will be: (Time period = 2 second)
1.
2.
3.
4.
The (displacement-time) graph of a particle executing SHM is shown in the figure. Then,
a. | the force is zero at \(t=\frac{3T}{4}\) |
b. | the acceleration is maximum at \(t=\frac{4T}{4}\) |
c. | the velocity is maximum at \(t=\frac{T}{4}\) |
d. | the potential energy is equal to the kinetic energy of oscillation at \(t=\frac{T}{2}\) |
Which of the statement/s given above is/are true?
1. | (a), (b), (d) |
2. | (a), (b), (c) |
3. | (b), (c), (d) |
4. | (c), (d) |
A body is performing SHM, then its:
(a) average total energy per cycle is equal to its maximum kinetic energy.
(b) average kinetic energy per cycle is equal to half of its maximum kinetic energy.
(c) mean velocity for a complete cycle is equal to times of its maximum velocity.
(d) root mean square velocity is times of its maximum velocity.
Choose the correct alternatives:
1. (a, b, d)
2. (a, c)
3. (b, d)
4. (b, c, d)
Which of the following functions of time represent/s periodic motion? [ω is any positive constant]
(a) sinωt + cosωt
(b) sinωt + cos2ωt + sin4ωt
(c) e–ωt
(d) log(ωt)
(e) sin2ωt
1. (a)
2. (a), (b) and (d)
3. (a), (b) and (e)
4. All
Which of the following statements is/are correct.
a. | Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways is transverse and longitudinal, both. |
b. | Waves produced in a cylinder containing a liquid by moving its piston back and forth is longitudinal. |
c. | Waves produced by a motorboat sailing in water are transverse and longitudinal, both. |
d. | Ultrasonic waves in air produced by a vibrating quartz crystal are longitudinal. |
1. (a), (b) and (d)
2. (b) and (d)
3. (a), (c) and (d)
4. All are correct
Assertion (A): | When a pendulum is made to oscillate on the surface of the moon, its time period increases. |
Reason (R): | Moon is much smaller as compared to Earth. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |