The angular velocities of three bodies in simple harmonic motion are \(\omega_1, \omega_2, \omega_3\) with their respective amplitudes as \(A_1, A_2, A_3.\) 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. \(A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2\)
Subtopic:  Simple Harmonic Motion |
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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. \({2a \pi \over T}\)
Subtopic:  Simple Harmonic Motion |
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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. \(2 \pi \sqrt{K}\)
Subtopic:  Simple Harmonic Motion |
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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 \(t = 0~\text{s}~\text{and}~t = 2~\text{s}\).
2. Phase of the oscillator is the same at \(t = 2~\text{s}~\text{and}~t = 6~\text{s}\).
3. Phase of the oscillator is the same at \(t = 1~\text{s}~\text{and}~t = 7~\text{s}\).
4. Phase of the oscillator is the same at \(t = 1~\text{s}~\text{and}~t = 5~\text{s}\).
1. \(1,2~\text{and}~4\) 2. \(1~\text{and}~3\)
3. \(2~\text{and}~4\) 4. \(3~\text{and}~4\)
Subtopic:  Simple Harmonic Motion |
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The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
                

1. \(25~\text{Hz}\)
2. \(50~\text{Hz}\)
3. \(12.25~\text{Hz}\)
4. \(33.3~\text{Hz}\)

Subtopic:  Simple Harmonic Motion |
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If the time of mean position from amplitude (extreme) position is \(6\) seconds, then the frequency of SHM will be:
1. \(0.01~\text{Hz}\) 2. \(0.02~\text{Hz}\)
3. \(0.03~\text{Hz}\) 4. \(0.04~\text{Hz}\)
Subtopic:  Simple Harmonic Motion |
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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 \(\mathrm{x\text-}\)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. \(x \left( t \right) = B\) \(\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)

Subtopic:  Simple Harmonic Motion | Phasor Diagram |
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