When a mass \(m\) is connected individually to two springs \(S_1\) and \(S_2,\) the oscillation frequencies are \(v_1\) and \(v_2.\) If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be:
1. | \(v_2+v_2\) | 2. | \(\sqrt{v_1^2+v_2^2}\) |
3. | \(\left(\dfrac{1}{v_1}+\dfrac{1}{v_1}\right)^{-1}\) | 4. | \(\sqrt{v_1^2-v_2^2}\) |
Two pendulums suspended from the same point have lengths of \(2\) m and \(0.5\) m. If they are displaced slightly and released, then they will be in the same phase when the small pendulum has completed:
1. \(2\) oscillations
2. \(4\) oscillations
3. \(3\) oscillations
4. \(5\) oscillations
1. | \(0.01~\text{Hz}\) | 2. | \(0.02~\text{Hz}\) |
3. | \(0.03~\text{Hz}\) | 4. | \(0.04~\text{Hz}\) |
A particle executing simple harmonic motion of amplitude \(5~\text{cm}\) has a maximum speed of \(31.4~\text{cm/s}.\) The frequency of its oscillation will be:
1. \(1~\text{Hz}\)
2. \(3~\text{Hz}\)
3. \(2~\text{Hz}\)
4. \(4~\text{Hz}\)
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.
The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is:
1. | the mean position |
2. | an extreme position |
3. | between the mean position and the positive extreme |
4. | between the mean position and the negative extreme |
The average energy in one time period in simple harmonic motion is:
1. \(\dfrac{1}{2} m \omega^{2} A^{2}\)
2. \(\dfrac{1}{4} m \omega^{2} A^{2}\)
3. \(m \omega^{2} A^{2}\)
4. zero
A spring-mass system oscillates with a frequency \(\nu.\) If it is taken in an elevator slowly accelerating upward, the frequency will:
1. increase
2. decrease
3. remain same
4. become zero