A small block of mass \(m\) slides a distance \(L\) down a smooth incline and rebounds elastically back up. The period of the motion is: (using standard symbols where necessary)
 
1. \(\sqrt{\dfrac{4L\sin\theta}{g}} \) 2. \(\sqrt{\dfrac{8L\sin\theta}{g}} \)
3. \(\sqrt{\dfrac{8L}{g\sin\theta}} \) 4. \(\sqrt{\dfrac{4L}{g\sin\theta}} \)
Subtopic:  Linear SHM |
Level 3: 35%-60%

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A particle moves in the x-y plane according to the equation
       \(x = A \cos^2 \omega t\) and \(y = A \sin^2 \omega t\)
Then, the particle undergoes:

1. uniform motion along the line \(x + y = A\)
2. uniform circular motion along \(x^2 + y^2 = A^2\)
3. SHM along the line \(x + y = A\)
4. SHM along the circle \(x^2 + y^2 = A^2\)
Subtopic:  Linear SHM |
Level 3: 35%-60%

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The equation of motion of a particle that starts moving at \(t=0\) s is given by \({x}=5 \sin \left(\dfrac{\pi t}{2}+\dfrac{\pi}{3}\right) \) where \(x\) is in cm and time \(t\) is in second. The time, when the particle first comes to rest, is:

1. \(\dfrac{1}{3}\) s 2. \(\dfrac{7}{6}\) s
3. \(\dfrac{2}{3}\) s 4. \(\dfrac{13}{6}\) s
Subtopic:  Linear SHM |
 63%
Level 2: 60%+

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