1. \(x= 10\sin\left(\pi t+\frac{\pi}{6}\right)\)
2. \(x= 10\sin\left(\pi t\right)\)
3. \(x= 10\cos\left(\pi t\right)\)
4. \(x= 5\sin\left(\pi t+\frac{\pi}{6}\right)\)
1. \(25~\text{Hz}\)
2. \(50~\text{Hz}\)
3. \(12.25~\text{Hz}\)
4. \(33.3~\text{Hz}\)
The (displacement-time) graph of a particle executing SHM is shown in the figure. Then,
(a) | the force is zero at \(t=\dfrac{3T}{4}\) |
(b) | the acceleration is maximum at \(t=\dfrac{4T}{4}\) |
(c) | the velocity is maximum at \(t=\dfrac{T}{4}\) |
(d) | the potential energy is equal to the kinetic energy of oscillation at \(t=\dfrac{T}{2}\) |
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 \(\dfrac{2}{\pi}\) times of its maximum velocity. |
(d) | root mean square velocity is \(\dfrac{1}{\sqrt{2}}\) times of its maximum velocity. |
Choose the correct alternatives:
1. (a), (b), (d)
2. (a), (c)
3. (b), (d)
4. (b), (c), (d)
(a) | \(\sin\omega t+ \cos \omega t\) |
(b) | \(\sin\omega t+ \cos 2\omega t+ \sin4\omega t\) |
(c) | \(e^{-\omega t}\) |
(d) | \(\mathrm{log(\omega t)}\) |
(e) | \(\sin^{2}\omega t\) |
Choose the correct alternatives:
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
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
1. | 2. | ||
3. | 4. |
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. |