A particle is attached to a vertical spring and pulled down a distance of \(0.01~\text{m}\) below its mean position and released. If its initial acceleration is \(0.16~\text{m/s}^2\), then its time period in seconds will be:
1. \(\pi\)
2. \(\frac{\pi}{2}\)
3. \(\frac{\pi}{4}\)
4. \(2\pi\)

Subtopic:  Spring mass system |
 89%
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A particle is executing linear simple harmonic motion with an amplitude \(a\) and an angular frequency \(\omega.\) Its average speed for its motion from extreme to mean position will be:
1. \(\dfrac{a\omega}{4}\)
2. \(\dfrac{a\omega}{2\pi}\)
3. \(\dfrac{2a\omega}{\pi}\)
4. \(\dfrac{a\omega}{\sqrt{3}\pi}\)

Subtopic:  Linear SHM |
 57%
From NCERT
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Two simple harmonic motions, \(y_1 = a \sin\omega t\) and \(y_2 = 2a\sin\left(\omega t+\frac{2\pi}{3}\right)\) are superimposed on a particle of mass \(m\). The maximum kinetic energy of the particle will be:
1. \(\frac{1}{2}m\omega^2a^2\)
2. \(\frac{5}{4}m\omega^2a^2\)
3. \(\frac{3}{2}m\omega^2a^2\)
4. Zero
Subtopic:  Energy of SHM |
 60%
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All the surfaces are smooth and springs are ideal. If a block of mass \(m\) is given the velocity \(v_0\) in the right direction, then the time period of the block shown in the figure will be:

                       
1. \(\frac{12l}{v_0}\)
2. \(\frac{2l}{v_0}+ \frac{3\pi}{2}\sqrt{\frac{m}{k}}\)
3. \(\frac{4l}{v_0}+ \frac{3\pi}{2}\sqrt{\frac{m}{k}}\)
4. \( \frac{\pi}{2}\sqrt{\frac{m}{k}}\)

Subtopic:  Spring mass system |
 53%
From NCERT
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In a spring pendulum, in place of mass, a liquid is used. If liquid leaks out continuously, then the time period of the spring pendulum:
1. decreases continuously
2. increases continuously
3. first increases and then decreases
4. first decreases and then increases

Subtopic:  Spring mass system |
 53%
From NCERT
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Equation of a simple harmonic motion is given by \(x= a\sin \omega t\). For which value of \(x\), kinetic energy is equal to the potential energy?
1. \(x = \pm a\)
2. \(x = \pm \frac{a}{2}\)
3. \(x = \pm \frac{a}{\sqrt{2}}\)
4. \(x = \pm \frac{\sqrt{3}a}{2}\)
Subtopic:  Energy of SHM |
 83%
From NCERT
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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. \(\frac{T}{6}\)

Subtopic:  Phasor Diagram |
 50%
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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.
Subtopic:  Linear SHM |
 68%
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A particle executes linear SHM between \(x=A.\) The time taken to go from \(0\) to \(A/2\) is \(T_1\) and to go from \(A/2\) to \(A\) is \(T_2\) then:
1. \(T_1<T_2\) 2. \(T_1>T_2\)
3. \(T_1=T_2\) 4. \(T_1= 2T_2\)
Subtopic:  Linear SHM |
 74%
From NCERT
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Two simple pendulums of length \(1~\text{m}\) and \(16~\text{m}\) 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. \(\frac{3T}{2}\)
2. \(\frac{3T}{4}\)
3. \(\frac{2T}{3}\)
4. \(\frac{4T}{3}\)
Subtopic:  Angular SHM |
From NCERT
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