The time period of the given spring-mass system is:
1. \(2\pi \sqrt{\frac{m}{k}}\)
2. \(2\pi \sqrt{\frac{m}{2k}}\)
3. \(2\pi \sqrt{\frac{2m}{\sqrt{3}k}}\)
4. \(\pi \sqrt{\frac{m}{k}}\)
The equation of simple harmonic motion is given by X = (4 cm), then maximum velocity of the particle in simple harmonic motion is:
1. 25.12 m/s
2. 25.12 cm/s
3. 12.56 m/s
4. 12.56 cm/s
A spring pendulum is on the rotating table. The initial angular velocity of the table is \(\omega_{0}\) and the time period of the pendulum is \(T_{0}.\) Now the angular velocity of the table becomes \(2\omega_{0},\) then the new time period will be:
1. \(2T_{0}\)
2. \(T_0\sqrt{2}\)
3. remains the same
4. \(\frac{T_0}{\sqrt{2}}\)
If the vertical spring-mass system is dipped in a non-viscous liquid, then:
1. | only mean position is changed. |
2. | only the time period is changed. |
3. | time period and mean position both are changed. |
4. | time period and mean position both remain the same. |
The displacement \( x\) of a particle varies with time \(t\) as \(x = A sin\left (\frac{2\pi t}{T} +\frac{\pi}{3} \right)\). The time taken by the particle to reach from \(x = \frac{A}{2} \) to \(x = -\frac{A}{2} \) will be:
1. | \(\frac{T}{2}\) | 2. | \(\frac{T}{3}\) |
3. | \(\frac{T}{12}\) | 4. | \(\frac{T}{6}\) |
Force on a particle F varies with time t as shown in the given graph. The displacement x vs time t graph corresponding to the force-time graph will be:
1. | 2. | ||
3. | 4. |
The time period of a simple pendulum in a stationary trolley is \(T_1.\) If the trolley is moving with a constant speed, then time period is \(T_2,\) then:
1. \(T_1>T _2\)
2. \(T_1<T _2\)
3. \(T_1=T _2\)
4. \(T_2= \infty \)
A particle executes SHM with a frequency of \(20\) Hz. The frequency with which its potential energy oscillates is:
1. \(5\) Hz
2. \(20\) Hz
3. \(10\) Hz
4. \(40\) Hz
A particle is moving along the x-axis. The speed of particle v varies with position x as . The time period of S.H.M is
1.
2.
3.
4.
A block of mass m is attached to a massless spring having a spring constant k. The other end of the spring is fixed from the wall of a trolley, as shown in the figure. Spring is initially unstretched and the trolley starts moving toward the direction shown. Its velocity-time graph is also shown.
The energy of oscillation, as seen from the trolley is:
1.
2.
3.
4.