The graph between the velocity \((v)\) of a particle executing SHM and its displacement \((x)\) is shown in the figure. The time period of oscillation for this SHM will be:
1. \(\sqrt{\frac{\alpha}{\beta}}\)
2. \(2\pi\sqrt{\frac{\alpha}{\beta}}\)
3. \(2\pi\left(\frac{\beta}{\alpha}\right)\)
4. \(2\pi\left(\frac{\alpha}{\beta}\right)\)
A simple pendulum attached to the ceiling of a stationary lift has a time period of 1 s. The distance y covered by the lift moving downward varies with time as y = 3.75 , where y is in meters and t is in seconds. If g = 10 , then the time period of the pendulum will be:
1. | 4 s | 2. | 6 s |
3. | 2 s | 4. | 12 s |
In a forced oscillation, when the system oscillates under the action of the driving force in addition to its internal restoring force, the particle oscillates with a frequency equal to
1. The natural frequency of the body
2. Frequency of driving force
3. The difference in frequency of driving force and natural frequency
4. Mean of the driving frequency and natural frequency
A body executes oscillations under the effect of a small damping force. If the amplitude of the body reduces by 50% in 6 minutes, then amplitude after the next 12 minutes will be [initial amplitude is ] -
1.
2.
3.
4.
1. | the gravity of the earth | 2. | the mass of the block |
3. | spring constant | 4. | both (2) & (3) |
Acceleration of the particle at \(t = \frac{8}{3}~\text{s}\) from the given displacement \((y)\) versus time \((t)\) graph will be?
1. \(\frac{\sqrt{3}\pi^2}{4}~\text{cm/s}^2\)
2. \(-\frac{\sqrt{3}\pi^2}{4}~\text{cm/s}^2\)
3. \(-\pi^2~\text{cm/s}^2\)
4. zero
1. | \(T_1<T_2\) | 2. | \(T_1>T_2\) |
3. | \(T_1=T_2\) |
4. | \(T_1= 2T_2\) |
A particle executes simple harmonic oscillations under the effect of small damping. If the amplitude of oscillation becomes half of the initial value of 16 mm in five minutes, then what will be the amplitude after fifteen minutes?
1. 8 mm
2. 4 mm
3. 2 mm
4. 1 mm