Periodic, Oscillatory motion and its characteristics and types of SHM PYQs: JEE Mains Physics

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1. 1. A particle is executing simple harmonic motion. Its amplitude is \(A\) and time period is \(5\) sec. The time required by it to move from \(x = A\) to \(x = \dfrac{A}{\sqrt{2}}\) is _______ sec. 2026 Medium
2. 2. A uniform disc of radius \(R\) and mass \(M\) is free to oscillate about the axis \(A\) as shown in the figure. For small oscillations the time period is ______.
   (\(g\) is acceleration due to gravity)
   2026 Hard
3. 3. An object of uniform density rolls up the curved path with the initial velocity \(v_0\) as shown in the figure. If the maximum height attained by an object is \(\dfrac{7v_0^2}{10g}\) (\(g\) = acceleration due to gravity), the object is a _______.
   2026 Medium
4. 4. Match List-I with List-II.
   

   List-I	List-II
   A. \(\sin^2 \omega t\)	I. Periodic with time period \(T = \dfrac{\pi}{\omega}\) but not simple harmonic motion (SHM)
   B. \(\sin^3(2\omega t)\)	II. Periodic with time period \(T = \dfrac{2\pi}{\omega}\) but Not SHM
   C. \(\sin(\omega t) + \cos(\pi \omega t)\)	III. Periodic with time period \(T = \dfrac{\pi}{\omega}\) and SHM
   D. \(\cos\omega t + \cos 2\omega t\)	IV. Non-periodic

   
   Choose the correct answer from the options given below : 2026 Hard
5. 5. A particle executes simple harmonic motion and is located at \(x = a, b\)  and  \(c\) at times \(t_0, 2t_0\) and \(3t_0\) respectively. The frequency of the oscillation is 2018 Hard
6. 6. Which of the following expressions corresponds to simple harmonic motion along a straight line, where \(x\) is the displacement and \(a, b, c\) are positive constants? 2014 Medium

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