The angular velocities of three bodies in simple harmonic motion are with their respective amplitudes as . If all the three bodies have the same mass and maximum velocity, then:
1. | \(A_1 \omega_1=A_2 \omega_2=A_3 \omega_3\) |
2. | \(A_1 \omega_1^2=A_2 \omega_2^2=A_3 \omega_3^2\) |
3. | \(A_1^2 \omega_1=A_2^2 \omega_2=A_3^2 \omega_3\) |
4. | \(A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2\) |
An SHM has an amplitude \(a\) and a time period \(T.\) The maximum velocity will be:
1. \({4a \over T}\)
2. \({2a \over T}\)
3. \({2 \pi \over T}\)
4. \({2a \pi \over T}\)
The equation of motion of a particle is \({d^2y \over dt^2}+Ky=0 \) where \(K\) is a positive constant. The time period of the motion is given by:
1. | \(2 \pi \over K\) | 2. | \(2 \pi K\) |
3. | \(2 \pi \over \sqrt{K}\) | 4. | \(2 \pi \sqrt{K}\) |
Displacement versus time curve for a particle executing SHM is shown in the figure. Choose the correct statement/s.
1. | Phase of the oscillator is the same at t =0 s and t = 2 s. |
2. | Phase of the oscillator is the same at t =2 s and t=6 s. |
3. | Phase of the oscillator is the same at t = 1 s and t=7 s. |
4. | Phase of the oscillator is the same at t=1 s and t=5 s. |
1. | 1, 2 and 4 | 2. | 1 and 3 |
3. | 2 and 4 | 4. | 3 and 4 |
The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
1. 25 Hz
2. 50 Hz
3. 12.25 Hz
4. 33.3 Hz
If the time of mean position from amplitude (extreme) position is 6 seconds, then the frequency of SHM will be:
1. | \(0.01\) Hz | 2. | \(0.02\) Hz |
3. | \(0.03\) Hz | 4. | \(0.04\) Hz |
The figure shows the circular motion of a particle. The radius of the circle, the period, the sense of revolution, and the initial position are indicated in the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle \(P\) will be:
1. \(x \left( t \right) = B\) \(\text{sin} \left(\dfrac{2 πt}{30}\right)\)
2. \(x \left( t \right) = B\) \(\text{cos} \left(\dfrac{πt}{15}\right)\)
3. \(x \left( t \right) = B\) \(\text{sin} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)
4. \(x \left( t \right) = B\) \(\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)