Two spherical bobs of masses \(M_A\) and \(M_B\) are hung vertically from two strings of length \(l_A\) and \(l_B\) respectively. If they are executing SHM with frequency as per the relation \(f_A=2f_B,\) Then:
1. \(l_A = \frac{l_B}{4}\)
2. \(l_A= 4l_B\)
3. \(l_A= 2l_B~\&~M_A=2M_B\)
4. \(l_A= \frac{l_B}{2}~\&~M_A=\frac{M_B}{2}\)
A spring elongates by a length 'L' when a mass 'M' is suspended to it. Now a tiny mass 'm' is attached to the mass 'M' and then released. The new time period of oscillation will be:
1. \(2 \pi \sqrt{\frac{\left(\right. M + m \left.\right) l}{Mg}}\)
2. \(2 \pi \sqrt{\frac{ml}{Mg}}\)
3. \(2 \pi \sqrt{L / g}\)
4. \(2 \pi \sqrt{\frac{Ml}{\left(\right. m + M \left.\right) g}}\)
The frequency of a simple pendulum in a free-falling lift will be:
1. zero
2. infinite
3. can't say
4. finite
When a mass is suspended separately by two different springs, in successive order, then the time period of oscillations is \(t _1\) and \(t_2\) respectively. If it is connected by both springs as shown in the figure below, then the time period of oscillation becomes \(t_0.\) The correct relation between \(t_0,\) \(t_1\) & \(t_2\) is:
1.
2.
3.
4.
A particle of mass \(m\) oscillates with simple harmonic motion between points \(x_1\) and \(x_2\), the equilibrium position being \(O\). Its potential energy is plotted. It will be as given below in the graph:
1. | 2. | ||
3. | 4. |
The potential energy of a simple harmonic oscillator, when the particle is halfway to its endpoint, will be:
1. \(\frac{2E}{3}\)
2. \(\frac{E}{8}\)
3. \(\frac{E}{4}\)
4. \(\frac{E}{2}\)
1. | \(140 \text{ cm} / \text{s}^2 \) | 2. | \(160 \text{ m} / \text{s}^2 \) |
3. | \(140 \text{ m} / \text{s}^2 \) | 4. | \(14 \text{ m} / \text{s}^2\) |
1. | \(0.01~\text{Hz}\) | 2. | \(0.02~\text{Hz}\) |
3. | \(0.03~\text{Hz}\) | 4. | \(0.04~\text{Hz}\) |
1. | \(e^{\omega t}\) | 2. | \(\text{log}_e(\omega t)\) |
3. | \(\text{sin}\omega t+ \text{cos}\omega t\) | 4. | \(e^{-\omega t}\) |
1. | Phase of the oscillator is the same at \(t = 0~\text{s}~\text{and}~t = 2~\text{s}\). |
2. | Phase of the oscillator is the same at \(t = 2~\text{s}~\text{and}~t = 6~\text{s}\). |
3. | Phase of the oscillator is the same at \(t = 1~\text{s}~\text{and}~t = 7~\text{s}\). |
4. | Phase of the oscillator is the same at \(t = 1~\text{s}~\text{and}~t = 5~\text{s}\). |
1. | \(1,2~\text{and}~4\) | 2. | \(1~\text{and}~3\) |
3. | \(2~\text{and}~4\) | 4. | \(3~\text{and}~4\) |