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The figure shows the displacement time graph of a particle executing S.H.M. If the time period of oscillation is 2s the equation of motion of its SHM is 

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Important Questions on Simple Harmonic Motion

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 4
Two particles execute SHM of the same amplitude and frequency along the same straight line. They pass one another when going in opposite directions each time their displacement is half their amplitude. What is the phase difference between them?
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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 5
A small mass executes linear S.H.M. about O with amplitude 'a' and period T. Its displacement from O at time T/8 after passing through O is
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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 6
Two particles A and B perform SHM along the same straight line with the same amplitude 'a', same frequency 'f' and same equilibrium position 'O'. The greatest distance between them is found to be 3a/2. At some instant of time they have the same displacement from mean position. What is this displacement?
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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 7
A particle executes S.H.M. along a straight line with mean position x=0, period 20s and amplitude 5cm. The shortest time taken by the particle to go from x=4cm to x=-3cm is
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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 8
A particle performing S.H.M. is found at its equilibrium at t=1s and it is found to have a speed of 0.25 m s-1 at t=2s. If the period of oscillation is 6s Calculate amplitude of oscillation
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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 9

The diagram shows two oscillations. What is the phase difference between the oscillations?

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 10
An object of mass m is attached to a spring. The restoring force of the spring is F=-λx3, where x is the displacement. The oscillation period depends on the mass, λ and oscillation amplitude. Suppose the object is initially at rest. If the initial displacement is D then its period is τ. If the initial displacement is 2D, find the period. (Hint: use dimension analysis.)
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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 11
A particle executes S.H.M. in a straight line. In the first second starting from rest it travels a distance 'a' and in the next second a distance 'b' in the same direction. The amplitude of S.H.M. will be