Q. No.A partricle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then, its time period of vibration will be
(1)β2/α2
(2)α/β
(3)β2/α
(4)2πβ/α
The damping force on an oscillator is directly proportional to the velocity.The units of the constant of proportionality are
(1)
(2)
(3)
(4)
| 1. | simple harmonic motion of frequency \(\frac{\omega}{\pi}\). |
| 2. | simple harmonic motion of frequency \(\frac{3\omega}{2\pi}\). |
| 3. | non-simple harmonic motion. |
| 4. | simple harmonic motion of frequency \(\frac{\omega}{2\pi}\). |
The period of oscillation of a mass \(M\) suspended from a spring of negligible mass is \(T.\) If along with it another mass \(M\) is also suspended, the period of oscillation will now be:
1. \(T\)
2. \(T/\sqrt{2}\)
3. \(2T\)
4. \(\sqrt{2} T\)
1. \(\frac{\pi a\sqrt{3}}{2T}\)
2. \(\frac{\pi a}{T}\)
3. \(\frac{3\pi^2 a}{T}\)
4. \(\frac{\pi a\sqrt{3}}{T}\)
1. Acceleration \(=-k_0x+k_1x^2\)
2. Acceleration \(=-k(x+a)\)
3. Acceleration \(=k(x+a)\)
4. Acceleration \(=kx\)
Two simple harmonic motions of angular frequency \(100~\text{rad s}^{-1}\) and \(1000~\text{rad s}^{-1}\) have the same displacement amplitude. The ratio of their maximum acceleration will be:
1. \(1:10\)
2. \(1:10^{2}\)
3. \(1:10^{3}\)
4. \(1:10^{4}\)
A point performs simple harmonic oscillation of period T and the equation of motion is given by x= a sin .After the elapse of what fraction of the time period the velocity of the point will be equal to half to its maximum velocity?
(1)
(2)
(3)
(4)
1. \({4a \over T}\)
2. \({2a \over T}\)
3. \({2 \pi \over T}\)
4. \({2a \pi \over T}\)
1. \(1:2\)
2. \(2:1\)
3. \(2:3\)
4. \(3:2\)
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