A simple pendulum is pushed slightly from its equilibrium towards the left and then set free to execute the simple harmonic motion. Select the correct graph between its velocity (\(v\)) and displacement (\(x \)).
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1. | maybe \(K_0\) |
2. | must be \(K_0\) |
3. | may be more than \(K_{0}\) |
4. | both (1) and (3) |
The time period of the spring-mass system depends upon:
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
Acceleration-time (\(a\text-t\)) graph for a particle performing SHM is shown in the figure. Select the incorrect statement.
1. | Displacement of a particle at \(A\) is negative. |
2. | The potential energy of the particle at \(C\) is minimum. |
3. | The velocity of the particle at \(B\) is positive. |
4. | Speed of particle at \(D\) is decreasing. |
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. \(2\pi\left(\frac{\alpha}{\beta}\right)\)
Two simple pendulums of length 1 m and 16 m are in the same phase at the mean position at any instant. If T is the time period of the smaller pendulum, then the minimum time after which they will again be in the same phase will be:
1.
2.
3.
4.
1. | \(T_1<T_2\) | 2. | \(T_1>T_2\) |
3. | \(T_1=T_2\) |
4. | \(T_1= 2T_2\) |
A spring-block system oscillates with a time period \(T\) on the earth's surface. When the system is brought into a deep mine, the time period of oscillation becomes \(T'.\) Then one can conclude that:
1. \(T'>T\)
2. \(T'<T\)
3. \(T'=T\)
4. \(T'=2T\)