A mass is connected to a spring and it vibrates up and down, forming a simple harmonic system. Which of the following is/are correct?
(a) | The kinetic energy of the mass is at a maximum halfway up. |
(b) | The potential energy of the system is at a maximum at the top of the mass's motion. |
(c) | The potential energy of the system is at a maximum at the bottom of the mass's motion. |
1. | (a), (b) and (c) |
2. | (a) and (b) only |
3. | (b) only |
4. | (c) only |
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. | \(A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2\) |
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
1. | \(2 \pi \over K\) | 2. | \(2 \pi K\) |
3. | \(2 \pi \over \sqrt{K}\) | 4. | \(2 \pi \sqrt{K}\) |
On a smooth inclined plane, a body of mass \(M\) is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant \(K\), the period of oscillation of the body (assuming the springs as massless) will be:
1. \(2\pi \left( \frac{M}{2K}\right)^{\frac{1}{2}}\)
2. \(2\pi \left( \frac{2M}{K}\right)^{\frac{1}{2}}\)
3. \(2\pi \left(\frac{Mgsin\theta}{2K}\right)\)
4. \(2\pi \left( \frac{2Mg}{K}\right)^{\frac{1}{2}}\)
An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially un-stretched. Then the maximum extension in the spring will be:
1. 4 Mg/K
2. 2 Mg/K
3. Mg/K
4. Mg/2K
1. \(25~\text{Hz}\)
2. \(50~\text{Hz}\)
3. \(12.25~\text{Hz}\)
4. \(33.3~\text{Hz}\)